Large groups of automorphisms of compact Riemann surfaces of genus 2 to 101 --------------------------------------------------------------------------- Found by Marston Conder (University of Auckland) with the help of the "LowIndexNormalSubgroups" routine in Magma, in August 2010. ******************************************************************************** * Note: Some details about reflexibility were corrected in February 2015. * * The previous incorrect version can be found at Marston Conder's webpage * * www.math.auckland.ac.nz/~conder/BigSurfaceActions-2to101-ByGenus-Wrong.txt * ******************************************************************************** Here "large" means the group G of orientation-preserving automorphisms has order |G| > 4(g-1), where g is the genus of the Riemann surface. This list is ordered by the *genus* of the Riemann surface. In each case the group G is a quotient F/K, where K is a torsion-free normal subgroup of the Fuchsian group F that defines the action, with triangular or quadrangular signature. This subgroup K is the kernel of a smooth epimorphism from F to G, and has index |F:K| = |G| (the order of G). An indication is given as to whether the action is reflexible, or chiral, and in the reflexible case, whether there's a corresponding action of G on a compact non-orientable surface of (non-orientable) genus g+1. In the triangular case, an action is called "reflexible [m]" if the action of the group G extends to the action of a larger group G* (of twice the order of |G|), with extended triangular signature (of the form (0; +; [-]; {(p,q,r)})). When this happens the corresponding orientably-regular map is reflexible. On the other hand, an action is called "reflexible [n]" if the action of the group G extends to the action of a larger group G* (of twice the order of |G|), with signature of the form (0; +; [p]; {(q)}), where the triangular signature for G is either (0; +; [p,p,q]; {-}) or (0; +; [q,p,p]; {-}). The action is called "reflexible [m,n]" if both kinds of reflexibility occur. Similarly, in the quadrangular case, there are three different kinds of reflexibility that can occur, according as to which of the following is the signature type of the action of the larger group G*: [1] Signature (0; +; [-]; {(p,q,r,s)}) [2] Signature (0; +; [p]; {(q,r)}), where the quadrangular signature for G is either (0; +; [p,q,p,r]; {-}) or (0; +; [q,p,r,p]; {-}) [3] Signature (0; +; [p,q]; {(1)}), where the quadrangular signature for G is (0; +; [p,p,q,q]; {-}). The expressions in square brackets following the description of each group action are defining relators for the group G (in terms of three generators G.1, G.2 and G.3 in the triangular case, or four generators G.1, G.2, G.3 and G.4 in the quadrangular case). These are also normal generators for the kernel K -- that is, K is their normal closure. Following the group actions for each given genus, a note is made of (a) the largest group action preserving orientation, (b) the largest group action that would occur if we allowed orientation-reversing automorphisms as well, (c) the largest reflexible group action, (d) the largest chiral (irreflexible) group action, (e) the largest group action on a non-orientable surface of genus g+1, together with the type(s) of the largest group actions in each case. Marston Conder February 2015 Genus 2 actions: Genus 2 action of group of order 48 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 2 action of group of order 24 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^6 ] Genus 2 action of group of order 16 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 2 action of group of order 10 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-5 ] Genus 2 action of group of order 12 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^6 ] Genus 2 action of group of order 8 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^3 * G.3^-1 ] Genus 2 action of group of order 24 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 ] Genus 2 action of group of order 12 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.2^4 ] Genus 2 action of group of order 6 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.2^-1, G.3 * G.2^-1 ] Genus 2 action of group of order 8 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.3^-1 * G.1^-1 * G.2 ] Genus 2 action of group of order 5 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.1^-2 * G.2^-1, G.2 * G.1^-1 * G.2, G.3 * G.1^-1 ] Genus 2 action of group of order 5 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.1^-2 * G.3^-1, G.3 * G.1^-1 * G.3, G.2 * G.1^-1 ] Genus 2 action of group of order 5 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.1^-2 * G.2, G.2^-1 * G.1^-1 * G.2^-1, G.3 * G.2^-1 ] Genus 2 action of group of order 12 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-3 ] Genus 2 action of group of order 12 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 ] Genus 2 action of group of order 12 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 ] Genus 2 action of group of order 8 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.4^-1 * G.1 * G.4^-1, (G.1 * G.2)^2, G.3 * G.2 * G.4 ] Genus 2 action of group of order 8 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.1 * G.4, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1 ] Genus 2 action of group of order 8 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.2 * G.1 * G.4, G.3 * G.2 * G.1 * G.4^-1 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.2 * G.1 * G.3, G.3^-1 * G.2 * G.1 * G.3^-1, G.4 * G.3^-1 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1^-1 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.1 * G.2^-1 * G.3 ] Genus 2 action of group of order 6 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1^-1, G.4 * G.2^-1 ] Largest orientation-preserving group for genus 2 has order 48 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 2 has order 96 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 2 has order 96 ... group action with signature (0; +; [-]; {(2,3,8)}) No chiral group action for genus 2 Largest non-orientable group for non-orientable genus 3 has order 12 ... group action with signature (0; +; [-]; {(2,2,2,3)}) Check total 25 : 0 chiral, 25 reflexible, with 8 non-orientable quotient actions Genus 3 actions: Genus 3 action of group of order 168 via triangle group [ 2, 3, 7 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 3 action of group of order 96 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 3 action of group of order 48 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 3 action of group of order 48 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^6 ] Genus 3 action of group of order 32 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 3 action of group of order 32 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-4 * G.1 * G.2 * G.3^-3 ] Genus 3 action of group of order 24 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 3 action of group of order 24 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^6 ] Genus 3 action of group of order 14 via triangle group [ 2, 7, 14 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-7 ] Genus 3 action of group of order 16 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-8 ] Genus 3 action of group of order 16 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^2 * G.3^-1 ] Genus 3 action of group of order 12 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^5 * G.3^-1 ] Genus 3 action of group of order 48 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 3 action of group of order 24 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 3 action of group of order 21 via triangle group [ 3, 3, 7 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1 * G.3 ] Genus 3 action of group of order 21 via triangle group [ 3, 3, 7 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 3 action of group of order 24 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^4 ] Genus 3 action of group of order 12 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^4 ] Genus 3 action of group of order 9 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^-2 * G.3 ] Genus 3 action of group of order 9 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^-2 * G.1 * G.2^-1 ] Genus 3 action of group of order 16 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.1^4, G.2^4 ] Genus 3 action of group of order 16 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.1^4, G.2^4 ] Genus 3 action of group of order 16 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^4 ] Genus 3 action of group of order 16 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2, G.1^4, G.2^4 ] Genus 3 action of group of order 12 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-3 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^3 ] Genus 3 action of group of order 24 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-3 ] Genus 3 action of group of order 16 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4 ] Genus 3 action of group of order 16 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4 ] Genus 3 action of group of order 16 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^4 ] Genus 3 action of group of order 16 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.2 * G.4 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, (G.1 * G.3)^2 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^3, G.2 * G.1^-1 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3 * G.1 * G.4, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.2^-1 * G.1 * G.2^-1 * G.4, G.4^-1 * G.1 * G.2^-1 * G.1, G.3 * G.1^-1 ] Genus 3 action of group of order 12 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.1 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3 ] Largest orientation-preserving group for genus 3 has order 168 ... group action with signature (0: +; [2,3,7]; {-}) Largest group with or without reflections for genus 3 has order 336 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest group with reflections for genus 3 has order 336 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest chiral group for genus 3 has order 24 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 4 has order 48 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 47 : 6 chiral, 41 reflexible, with 11 non-orientable quotient actions Genus 4 actions: Genus 4 action of group of order 72 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^2 * G.3^-4 ] Genus 4 action of group of order 120 via triangle group [ 2, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 4 action of group of order 72 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6 ] Genus 4 action of group of order 40 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-6 * G.1 * G.2 * G.3^-3 ] Genus 4 action of group of order 32 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-4 * G.1 * G.2^-1 * G.3^-3 ] Genus 4 action of group of order 60 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.3^-1 * G.2)^3 ] Genus 4 action of group of order 36 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^6 ] Genus 4 action of group of order 36 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^6 ] Genus 4 action of group of order 36 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 4 action of group of order 24 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^6 ] Genus 4 action of group of order 18 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-9 ] Genus 4 action of group of order 20 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-7 * G.3 ] Genus 4 action of group of order 16 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-7 * G.3 ] Genus 4 action of group of order 36 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 4 action of group of order 36 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.3^4 ] Genus 4 action of group of order 24 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.2 * G.1^-1 * G.3 ] Genus 4 action of group of order 15 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^-5 ] Genus 4 action of group of order 18 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^-6 ] Genus 4 action of group of order 18 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.2^-6 ] Genus 4 action of group of order 18 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2^2 * G.3^-1 ] Genus 4 action of group of order 20 via triangle group [ 4, 4, 5 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2 * G.1 * G.3 ] Genus 4 action of group of order 20 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 4 action of group of order 20 via triangle group [ 4, 4, 5 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-1 * G.2 * G.1 * G.3^-1 ] Genus 4 action of group of order 16 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3 * G.2 * G.1^-1 * G.3^2 ] Genus 4 action of group of order 36 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 ] Genus 4 action of group of order 36 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 4 action of group of order 36 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.4)^2 ] Genus 4 action of group of order 24 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 4 action of group of order 24 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 ] Genus 4 action of group of order 24 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^3 ] Genus 4 action of group of order 24 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 4 action of group of order 20 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5 ] Genus 4 action of group of order 20 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5 ] Genus 4 action of group of order 20 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-5 ] Genus 4 action of group of order 16 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.1 * G.4^-2 ] Genus 4 action of group of order 16 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^2 ] Genus 4 action of group of order 16 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4^2 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.1 * G.4 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2, G.4), G.3 * G.1^-1 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3 ] Genus 4 action of group of order 18 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.3)^2, G.4^-3 ] Largest orientation-preserving group for genus 4 has order 120 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 4 has order 240 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 4 has order 240 ... group action with signature (0; +; [-]; {(2,4,5)}) No chiral group action for genus 4 Largest non-orientable group for non-orientable genus 5 has order 120 ... group action with signature (0; +; [-]; {(2,4,5)}) Check total 47 : 0 chiral, 47 reflexible, with 17 non-orientable quotient actions Genus 5 actions: Genus 5 action of group of order 192 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 5 action of group of order 120 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.1 * G.3)^2 ] Genus 5 action of group of order 160 via triangle group [ 2, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^4 ] Genus 5 action of group of order 96 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 5 action of group of order 64 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^8 ] Genus 5 action of group of order 64 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4 ] Genus 5 action of group of order 48 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-12 ] Genus 5 action of group of order 40 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-6 * G.1 * G.2^-1 * G.3^-3 ] Genus 5 action of group of order 80 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.1 * G.2 * G.3^-2 ] Genus 5 action of group of order 48 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 5 action of group of order 30 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 5 action of group of order 32 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^8 ] Genus 5 action of group of order 32 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 5 action of group of order 22 via triangle group [ 2, 11, 22 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^2 * G.2^-8 ] Genus 5 action of group of order 24 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^3 * G.2^-7 * G.3 ] Genus 5 action of group of order 20 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-8 ] Genus 5 action of group of order 96 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 5 action of group of order 60 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 5 action of group of order 48 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 ] Genus 5 action of group of order 48 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2 ] Genus 5 action of group of order 48 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 5 action of group of order 24 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1)^2 ] Genus 5 action of group of order 32 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2 ] Genus 5 action of group of order 32 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1 ] Genus 5 action of group of order 32 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2 ] Genus 5 action of group of order 32 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 5 action of group of order 24 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^6 ] Genus 5 action of group of order 20 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^2 * G.2^-1 * G.1 * G.3^2 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.3 * G.1 * G.4 * G.2 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^4 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 5 action of group of order 48 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, (G.1 * G.2)^4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, (G.1 * G.3)^4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 5 action of group of order 32 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^4 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, (G.1 * G.3)^4 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^6 ] Genus 5 action of group of order 20 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^2 * G.3 * G.2 * G.4^2 ] Genus 5 action of group of order 20 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.4^2 ] Genus 5 action of group of order 20 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^2 * G.2 * G.1 * G.4^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^4, G.2 * G.1^-1 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.3 * G.4^-1)^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.1 * G.4, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1)^2, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^2 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2^-1 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3 ] Genus 5 action of group of order 24 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4, G.4^-3 ] Largest orientation-preserving group for genus 5 has order 192 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 5 has order 384 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 5 has order 384 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 5 has order 48 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 6 has order 160 ... group action with signature (0; +; [-]; {(2,4,5)}) Check total 83 : 12 chiral, 71 reflexible, with 31 non-orientable quotient actions Genus 6 actions: Genus 6 action of group of order 150 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-5 * G.1 * G.2^-2 * G.3^-4 ] Genus 6 action of group of order 120 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^6 ] Genus 6 action of group of order 72 via triangle group [ 2, 4, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 6 action of group of order 56 via triangle group [ 2, 4, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-9 * G.1 * G.2 * G.3^-4 ] Genus 6 action of group of order 48 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-8 * G.1 * G.2^-1 * G.3^-3 ] Genus 6 action of group of order 50 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 6 action of group of order 48 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^2 * G.2^2 * G.1 * G.3 ] Genus 6 action of group of order 48 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^8 ] Genus 6 action of group of order 36 via triangle group [ 2, 9, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^9 ] Genus 6 action of group of order 30 via triangle group [ 2, 10, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2^-2 * G.3^2 ] Genus 6 action of group of order 26 via triangle group [ 2, 13, 26 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^13 ] Genus 6 action of group of order 28 via triangle group [ 2, 14, 14 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^14 ] Genus 6 action of group of order 24 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^3 * G.2^-8 ] Genus 6 action of group of order 75 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 6 action of group of order 39 via triangle group [ 3, 3, 13 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 6 action of group of order 39 via triangle group [ 3, 3, 13 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 6 action of group of order 21 via triangle group [ 3, 7, 21 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^-1 * G.3 * G.2^-3 * G.3^2 ] Genus 6 action of group of order 24 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.2^-8 ] Genus 6 action of group of order 28 via triangle group [ 4, 4, 7 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^3 * G.2 * G.1 * G.3^3 ] Genus 6 action of group of order 24 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^2 * G.2 * G.1^-1 * G.3^3 ] Genus 6 action of group of order 24 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^2 * G.1 * G.3^-1 ] Genus 6 action of group of order 24 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.1^4, G.2^6 ] Genus 6 action of group of order 25 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.1^-5, G.2^-5 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.3 * G.1)^3 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 6 action of group of order 60 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 6 action of group of order 28 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-7 ] Genus 6 action of group of order 28 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4 * G.1^2 * G.4^3 ] Genus 6 action of group of order 28 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^4 * G.1^2 * G.4^3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.1 * G.4^-3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.4^3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^2 * G.2 * G.1 * G.4^3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.2 * G.4, G.3^-3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.1 * G.4, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3^-1)^2, G.3^-3, G.4^4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.2^-1 * G.4, G.4^-1 * G.1 * G.4^-1 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2^-1 * G.4, G.4 * G.1 * G.2 * G.3, (G.1 * G.4)^2, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.4^2 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, (G.2^-1 * G.3)^2, G.4^4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4, G.4^4, G.2 * G.3 * G.2^-1 * G.4^2 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.2^-1 * G.1, G.3 * G.1 * G.2 * G.4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.2 * G.3, G.4^4 ] Genus 6 action of group of order 24 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.3)^2, G.4^4 ] Largest orientation-preserving group for genus 6 has order 150 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 6 has order 300 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 6 has order 300 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 6 has order 60 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 7 has order 120 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 56 : 10 chiral, 46 reflexible, with 14 non-orientable quotient actions Genus 7 actions: Genus 7 action of group of order 504 via triangle group [ 2, 3, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 7 action of group of order 144 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 7 action of group of order 64 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 7 action of group of order 64 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-6 * G.1 * G.3^5 * G.2^-1 * G.3^-4 ] Genus 7 action of group of order 56 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-9 * G.1 * G.2^-1 * G.3^-4 ] Genus 7 action of group of order 54 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^3 * G.3^-1 * G.1 ] Genus 7 action of group of order 54 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2^2 * G.1 * G.3 ] Genus 7 action of group of order 54 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 7 action of group of order 48 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 7 action of group of order 42 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 7 action of group of order 56 via triangle group [ 2, 7, 7 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 ] Genus 7 action of group of order 56 via triangle group [ 2, 7, 7 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.1 * G.2^-3 * G.3^-2 * G.2 ] Genus 7 action of group of order 30 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^15 ] Genus 7 action of group of order 32 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^16 ] Genus 7 action of group of order 32 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^6 * G.3^-2 ] Genus 7 action of group of order 28 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^13 * G.3^-1 ] Genus 7 action of group of order 72 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 7 action of group of order 48 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 7 action of group of order 36 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 7 action of group of order 27 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1, G.2^2 * G.3^-1 * G.2^4 * G.3^-2 ] Genus 7 action of group of order 27 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-2 * G.1 * G.3 ] Genus 7 action of group of order 27 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.1 * G.2^-1 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^4 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 7 action of group of order 32 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2 ] Genus 7 action of group of order 28 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^3 * G.2 * G.1^-1 * G.3^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^4 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^4 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3 ] Genus 7 action of group of order 48 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, (G.4^-1 * G.2)^3 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 7 action of group of order 36 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-3 * G.1 * G.2 * G.4^3 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-4 * G.1^2 * G.4^-4 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.2 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 32 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 7 action of group of order 28 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^3 * G.3 * G.2 * G.4^3 ] Genus 7 action of group of order 28 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4^3 ] Genus 7 action of group of order 28 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^3 * G.2 * G.1 * G.4^3 ] Largest orientation-preserving group for genus 7 has order 504 ... group action with signature (0: +; [2,3,7]; {-}) Largest group with or without reflections for genus 7 has order 1008 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest group with reflections for genus 7 has order 1008 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest chiral group for genus 7 has order 54 ... group action with signature (0: +; [2,6,9]; {-}) Largest non-orientable group for non-orientable genus 8 has order 504 ... group action with signature (0; +; [-]; {(2,3,7)}) Check total 84 : 16 chiral, 68 reflexible, with 31 non-orientable quotient actions Genus 8 actions: Genus 8 action of group of order 336 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 8 action of group of order 336 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 8 action of group of order 72 via triangle group [ 2, 4, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-13 * G.1 * G.2 * G.3^-4 ] Genus 8 action of group of order 64 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-6 * G.1 * G.3^5 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 8 action of group of order 84 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 8 action of group of order 84 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 8 action of group of order 84 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 8 action of group of order 84 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 8 action of group of order 60 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 8 action of group of order 48 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 8 action of group of order 48 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 ] Genus 8 action of group of order 40 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^10 ] Genus 8 action of group of order 34 via triangle group [ 2, 17, 34 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^17 ] Genus 8 action of group of order 36 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^18 ] Genus 8 action of group of order 32 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^15 * G.3^-1 ] Genus 8 action of group of order 168 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 8 action of group of order 168 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 8 action of group of order 48 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2 ] Genus 8 action of group of order 42 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-2 * G.2^2 * G.3^-1 * G.2 ] Genus 8 action of group of order 42 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 8 action of group of order 42 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 8 action of group of order 42 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 8 action of group of order 30 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.2 * G.3^-1 * G.2^6 * G.3^-1 * G.2 ] Genus 8 action of group of order 36 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^5 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 8 action of group of order 32 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^4 * G.2^-1 * G.1 * G.3^3 ] Genus 8 action of group of order 30 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.3, G.1^-5, G.2^6 ] Genus 8 action of group of order 36 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 8 action of group of order 36 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.2 * G.4^3 ] Genus 8 action of group of order 36 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^9 ] Genus 8 action of group of order 32 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4 * G.3 * G.2 * G.4^3 ] Genus 8 action of group of order 32 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-4 * G.1 * G.3 * G.4^-3 ] Genus 8 action of group of order 32 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^3 * G.2 * G.1 * G.4^4 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.1 * G.4 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 8 action of group of order 30 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-5 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2^2 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2^2 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 8 action of group of order 42 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 8 action of group of order 30 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.3)^2, G.4^-5 ] Largest orientation-preserving group for genus 8 has order 336 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 8 has order 672 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 8 has order 672 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 8 has order 84 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 9 has order 336 ... group action with signature (0; +; [-]; {(2,3,8)}) Check total 66 : 32 chiral, 34 reflexible, with 14 non-orientable quotient actions Genus 9 actions: Genus 9 action of group of order 192 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 320 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 9 action of group of order 192 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 192 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 9 action of group of order 128 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8 ] Genus 9 action of group of order 128 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^8 ] Genus 9 action of group of order 128 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3 ] Genus 9 action of group of order 128 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 9 action of group of order 96 via triangle group [ 2, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 ] Genus 9 action of group of order 96 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.2 * G.3^-1)^4 ] Genus 9 action of group of order 96 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 9 action of group of order 80 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-15 * G.1 * G.2 * G.3^-4 ] Genus 9 action of group of order 72 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-13 * G.1 * G.2^-1 * G.3^-4 ] Genus 9 action of group of order 160 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 ] Genus 9 action of group of order 120 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6 ] Genus 9 action of group of order 120 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-2)^2 ] Genus 9 action of group of order 96 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 96 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.3^-1 * G.2)^3 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^8 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-3 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.2^-2 * G.3^3 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 64 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^8 ] Genus 9 action of group of order 48 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8 ] Genus 9 action of group of order 48 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 9 action of group of order 48 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-12 ] Genus 9 action of group of order 48 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^3 * G.3^-2, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 9 action of group of order 48 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3^2 * G.2^-6 * G.3^2 ] Genus 9 action of group of order 42 via triangle group [ 2, 14, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^3 ] Genus 9 action of group of order 38 via triangle group [ 2, 19, 38 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^8 * G.2^-10 ] Genus 9 action of group of order 40 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^9 * G.2^-9 * G.3 ] Genus 9 action of group of order 36 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^17 * G.3^-1 ] Genus 9 action of group of order 96 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 9 action of group of order 57 via triangle group [ 3, 3, 19 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 ] Genus 9 action of group of order 57 via triangle group [ 3, 3, 19 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 9 action of group of order 96 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3 ] Genus 9 action of group of order 96 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 9 action of group of order 48 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 9 action of group of order 60 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-5 ] Genus 9 action of group of order 60 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-5 ] Genus 9 action of group of order 48 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^4 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^4 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^2 * G.3 * G.2 ] Genus 9 action of group of order 64 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 9 action of group of order 48 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^4 ] Genus 9 action of group of order 48 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-1 * G.3 ] Genus 9 action of group of order 48 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1 * G.3, (G.2^-1 * G.1)^3 ] Genus 9 action of group of order 48 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^6 ] Genus 9 action of group of order 48 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6 ] Genus 9 action of group of order 40 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 9 action of group of order 40 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 9 action of group of order 40 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^6 * G.2 * G.1 * G.3^3 ] Genus 9 action of group of order 36 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^5 * G.2^-1 * G.1 * G.3^3 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 9 action of group of order 96 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 9 action of group of order 64 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.3)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, (G.1 * G.2)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, (G.1 * G.3)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.2)^4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^6 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^5 * G.3 * G.1 * G.2 * G.4^4 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-10 ] Genus 9 action of group of order 40 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^3 ] Genus 9 action of group of order 36 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-4 * G.2 * G.3 * G.4^-4 ] Genus 9 action of group of order 36 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.4^3 ] Genus 9 action of group of order 36 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^5 * G.2 * G.1 * G.4^3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.1 * G.2^-1)^3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 9 action of group of order 48 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Largest orientation-preserving group for genus 9 has order 320 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 9 has order 640 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 9 has order 640 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 9 has order 96 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 10 has order 192 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 186 : 28 chiral, 158 reflexible, with 54 non-orientable quotient actions Genus 10 actions: Genus 10 action of group of order 432 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 10 action of group of order 432 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 10 action of group of order 324 via triangle group [ 2, 3, 9 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 10 action of group of order 216 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^7 * G.2^-1 * G.1 * G.3^4 ] Genus 10 action of group of order 180 via triangle group [ 2, 3, 15 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.3^-4 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 162 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^6 * G.2 * G.3^-5 * G.1 ] Genus 10 action of group of order 144 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 10 action of group of order 360 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, (G.3^-1 * G.2)^5 ] Genus 10 action of group of order 216 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 10 action of group of order 216 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 10 action of group of order 168 via triangle group [ 2, 4, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^-3 * G.1 * G.2 * G.3^-3 ] Genus 10 action of group of order 144 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 10 action of group of order 144 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.2 ] Genus 10 action of group of order 108 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 88 via triangle group [ 2, 4, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-17 * G.1 * G.2 * G.3^-4 ] Genus 10 action of group of order 80 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-15 * G.1 * G.2^-1 * G.3^-4 ] Genus 10 action of group of order 108 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 10 action of group of order 108 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 ] Genus 10 action of group of order 108 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 10 action of group of order 108 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 72 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3 * G.2 * G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 10 action of group of order 72 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^6 ] Genus 10 action of group of order 72 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 10 action of group of order 60 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.1 * G.3^4 * G.2^-1 * G.3^-5 ] Genus 10 action of group of order 72 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 ] Genus 10 action of group of order 72 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 10 action of group of order 54 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9 ] Genus 10 action of group of order 48 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.2^2 * G.3^-2 ] Genus 10 action of group of order 42 via triangle group [ 2, 21, 42 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^10 * G.2^-10 ] Genus 10 action of group of order 44 via triangle group [ 2, 22, 22 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^11 * G.2^-9 * G.3 ] Genus 10 action of group of order 40 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^9 * G.2^-10 ] Genus 10 action of group of order 216 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 10 action of group of order 216 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 10 action of group of order 216 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 10 action of group of order 216 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 ] Genus 10 action of group of order 108 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 ] Genus 10 action of group of order 81 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 10 action of group of order 81 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 10 action of group of order 81 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 72 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 10 action of group of order 63 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 10 action of group of order 63 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^2 ] Genus 10 action of group of order 108 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 108 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 10 action of group of order 72 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3 ] Genus 10 action of group of order 54 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 10 action of group of order 54 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6 ] Genus 10 action of group of order 54 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 10 action of group of order 54 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, (G.3^-1 * G.2)^3 ] Genus 10 action of group of order 42 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.3^-2 * G.1^-1 * G.2^2 ] Genus 10 action of group of order 42 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 10 action of group of order 72 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 10 action of group of order 72 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 10 action of group of order 72 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 ] Genus 10 action of group of order 72 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 10 action of group of order 44 via triangle group [ 4, 4, 11 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^11 ] Genus 10 action of group of order 40 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^6 * G.2 * G.1^-1 * G.3^3 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^6, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 10 action of group of order 108 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 10 action of group of order 72 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-5, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-5 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^-5 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-5, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-5, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 10 action of group of order 60 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.4^2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^3 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^3 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 ] Genus 10 action of group of order 48 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 10 action of group of order 44 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 10 action of group of order 44 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-11 ] Genus 10 action of group of order 44 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^11 ] Genus 10 action of group of order 40 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^5 * G.3 * G.2 * G.4^4 ] Genus 10 action of group of order 40 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-6 * G.1 * G.3 * G.4^-3 ] Genus 10 action of group of order 40 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3^-1 * G.1 * G.3 * G.1)^3, G.2 * G.1^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, (G.2 * G.1)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2^2 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 10 action of group of order 54 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3 ] Largest orientation-preserving group for genus 10 has order 432 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 10 has order 720 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 10 has order 720 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 10 has order 432 ... group action with signature (0: +; [2,3,8]; {-}) Largest non-orientable group for non-orientable genus 11 has order 216 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 160 : 60 chiral, 100 reflexible, with 17 non-orientable quotient actions Genus 11 actions: Genus 11 action of group of order 240 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 11 action of group of order 160 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 11 action of group of order 160 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 160 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 160 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 11 action of group of order 120 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 11 action of group of order 120 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 11 action of group of order 96 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3^5 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 11 action of group of order 96 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-19 * G.1 * G.2 * G.3^-4 ] Genus 11 action of group of order 88 via triangle group [ 2, 4, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-17 * G.1 * G.2^-1 * G.3^-4 ] Genus 11 action of group of order 120 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-2 * G.2)^2, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 96 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 ] Genus 11 action of group of order 96 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 11 action of group of order 66 via triangle group [ 2, 6, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^6 * G.2^-1 * G.3^-4 * G.1 ] Genus 11 action of group of order 80 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8 ] Genus 11 action of group of order 80 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8 ] Genus 11 action of group of order 80 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 11 action of group of order 80 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 ] Genus 11 action of group of order 64 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 11 action of group of order 64 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 11 action of group of order 60 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.2^2 * G.3^-1 * G.2 ] Genus 11 action of group of order 60 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 11 action of group of order 46 via triangle group [ 2, 23, 46 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^12 * G.2^-10 ] Genus 11 action of group of order 48 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^13 * G.2^-9 * G.3 ] Genus 11 action of group of order 48 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3^2 * G.2^-8 ] Genus 11 action of group of order 44 via triangle group [ 2, 44, 44 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^11 * G.2^-10 ] Genus 11 action of group of order 120 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 11 action of group of order 48 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2 * G.1^-1 * G.2^-2, G.3^-2 * G.1^-1 * G.3 * G.2 ] Genus 11 action of group of order 48 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1 * G.2)^2 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 11 action of group of order 80 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 ] Genus 11 action of group of order 60 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 11 action of group of order 60 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 48 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 11 action of group of order 48 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^12 ] Genus 11 action of group of order 48 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3 ] Genus 11 action of group of order 48 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 11 action of group of order 44 via triangle group [ 4, 4, 22 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 11 action of group of order 48 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 11 action of group of order 48 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1, G.2^6 ] Genus 11 action of group of order 48 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 11 action of group of order 48 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^5 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^5 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^3 ] Genus 11 action of group of order 120 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 11 action of group of order 80 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-12 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-8 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^12 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 11 action of group of order 44 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5 * G.2 * G.3 * G.4^-5 ] Genus 11 action of group of order 44 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7 * G.1 * G.3 * G.4^-3 ] Genus 11 action of group of order 44 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^6 * G.2 * G.1 * G.4^4 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^5, G.2 * G.1^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, (G.3^-1 * G.1)^3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.4 * G.3 * G.1 * G.4 * G.3^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4 * G.3 * G.2 * G.4 * G.3^-1 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.3 * G.4^-1)^2, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.4^-1)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.3 * G.4^-1)^2, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, (G.2 * G.4^-1)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.3 * G.2^-1)^3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.2^-1)^3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.1 * G.2^-1)^3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 11 action of group of order 60 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, (G.2 * G.4^-1)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2^-1 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.1 * G.4, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1)^2, G.4^4 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 11 action of group of order 48 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Largest orientation-preserving group for genus 11 has order 240 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 11 has order 480 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 11 has order 480 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 11 has order 160 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 12 has order 240 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 182 : 88 chiral, 94 reflexible, with 50 non-orientable quotient actions Genus 12 actions: Genus 12 action of group of order 120 via triangle group [ 2, 4, 15 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 12 action of group of order 104 via triangle group [ 2, 4, 26 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-20 * G.1 * G.2 * G.3^-5 ] Genus 12 action of group of order 96 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-19 * G.1 * G.2^-1 * G.3^-4 ] Genus 12 action of group of order 110 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 12 action of group of order 110 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 12 action of group of order 110 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 12 action of group of order 110 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 ] Genus 12 action of group of order 84 via triangle group [ 2, 6, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 12 action of group of order 80 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 12 action of group of order 60 via triangle group [ 2, 10, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^10 ] Genus 12 action of group of order 56 via triangle group [ 2, 14, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-4 * G.3 * G.2^-7 * G.3 * G.2^-1 ] Genus 12 action of group of order 60 via triangle group [ 2, 15, 15 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-11 * G.3 * G.2^-1 ] Genus 12 action of group of order 50 via triangle group [ 2, 25, 50 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^14 * G.2^-10 ] Genus 12 action of group of order 52 via triangle group [ 2, 26, 26 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^15 * G.2^-9 * G.3 ] Genus 12 action of group of order 48 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^13 * G.2^-10 ] Genus 12 action of group of order 84 via triangle group [ 3, 3, 14 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 12 action of group of order 84 via triangle group [ 3, 3, 14 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 12 action of group of order 52 via triangle group [ 4, 4, 13 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 12 action of group of order 52 via triangle group [ 4, 4, 13 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-2 ] Genus 12 action of group of order 52 via triangle group [ 4, 4, 13 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^5 * G.2^-1 * G.1^-1 * G.3^7 ] Genus 12 action of group of order 48 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^5 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 12 action of group of order 48 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1 ] Genus 12 action of group of order 48 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.1^-2 * G.3 * G.2, G.2^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^2 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.1^-1 * G.2^-2 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.1^-2 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.1 * G.3^-1 * G.1^-1 * G.2^2 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3 * G.2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-2, G.3^-2 * G.1^-1 * G.2 * G.1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.1^-2 * G.2^-1 * G.3^-1, G.1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.1^-2 * G.3^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2 * G.1^-1 * G.3^2, G.3^-2 * G.1^-1 * G.2^2 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.1^-2 * G.2^2, G.2^2 * G.1^2 * G.3 * G.2 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.1^-2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.1^-2 * G.2 * G.3^-1, G.3 * G.2 * G.1^2 * G.3^2 ] Genus 12 action of group of order 55 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.1^-2 * G.3 * G.2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 ] Genus 12 action of group of order 52 via quadrangle group [ 2, 2, 2, 13 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-6 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 12 action of group of order 52 via quadrangle group [ 2, 2, 2, 13 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-13 ] Genus 12 action of group of order 52 via quadrangle group [ 2, 2, 2, 13 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-5 * G.1 * G.2 * G.1 * G.4^6 * G.2 ] Genus 12 action of group of order 48 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-6 * G.1 * G.4^-6 ] Genus 12 action of group of order 48 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-8 * G.2 * G.4^-4 ] Genus 12 action of group of order 48 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^7 * G.2 * G.1 * G.4^4 ] Largest orientation-preserving group for genus 12 has order 120 ... group action with signature (0: +; [2,4,15]; {-}) Largest group with or without reflections for genus 12 has order 240 ... group action with signature (0; +; [-]; {(2,4,15)}) Largest group with reflections for genus 12 has order 240 ... group action with signature (0; +; [-]; {(2,4,15)}) Largest chiral group for genus 12 has order 110 ... group action with signature (0: +; [2,5,10]; {-}) Largest non-orientable group for non-orientable genus 13 has order 120 ... group action with signature (0; +; [-]; {(2,4,15)}) Check total 41 : 16 chiral, 25 reflexible, with 9 non-orientable quotient actions Genus 13 actions: Genus 13 action of group of order 360 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 13 action of group of order 288 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-12 ] Genus 13 action of group of order 144 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3 ] Genus 13 action of group of order 128 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-5 * G.1 * G.3^5 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 13 action of group of order 128 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 13 action of group of order 112 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-22 * G.1 * G.2 * G.3^-5 ] Genus 13 action of group of order 104 via triangle group [ 2, 4, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-20 * G.1 * G.2^-1 * G.3^-5 ] Genus 13 action of group of order 120 via triangle group [ 2, 5, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 ] Genus 13 action of group of order 144 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 13 action of group of order 144 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 13 action of group of order 96 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^2 ] Genus 13 action of group of order 96 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 13 action of group of order 90 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.1 * G.3^9 * G.2 * G.3^-5 ] Genus 13 action of group of order 78 via triangle group [ 2, 6, 39 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-5 ] Genus 13 action of group of order 72 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9 ] Genus 13 action of group of order 72 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-3 * G.3^2 * G.2^-5 * G.3^2 ] Genus 13 action of group of order 72 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 13 action of group of order 72 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-2 * G.3 * G.2^-8 * G.3 ] Genus 13 action of group of order 64 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2^8 * G.3^-2 * G.2^2 * G.3^-1 * G.2 ] Genus 13 action of group of order 64 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^5 * G.3^-1 * G.2 * G.3^-1 ] Genus 13 action of group of order 64 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^5 * G.3^-1 * G.2 * G.3^-1 ] Genus 13 action of group of order 64 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-1 * G.2^4 * G.3^-3 ] Genus 13 action of group of order 54 via triangle group [ 2, 27, 54 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^16 * G.2^-10 ] Genus 13 action of group of order 56 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^17 * G.2^-9 * G.3 ] Genus 13 action of group of order 52 via triangle group [ 2, 52, 52 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^15 * G.2^-10 ] Genus 13 action of group of order 180 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^2 * G.2)^2 ] Genus 13 action of group of order 144 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3 * G.2)^2, G.3^6 ] Genus 13 action of group of order 96 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.3^-1 * G.2)^3 ] Genus 13 action of group of order 96 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 13 action of group of order 96 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.3^-1 * G.2)^3 ] Genus 13 action of group of order 96 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3 ] Genus 13 action of group of order 96 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3 ] Genus 13 action of group of order 72 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2 ] Genus 13 action of group of order 72 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 13 action of group of order 72 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.3 * G.2)^2 ] Genus 13 action of group of order 72 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 13 action of group of order 72 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, (G.2 * G.3^-2 * G.2)^2 ] Genus 13 action of group of order 72 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-3 * G.1 * G.3^4 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2, G.3 * G.2 * G.1^2 * G.3 * G.2^-1 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.3^2 ] Genus 13 action of group of order 64 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 13 action of group of order 56 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^6 * G.2^-1 * G.1^-1 * G.3^7 ] Genus 13 action of group of order 52 via triangle group [ 4, 4, 26 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^5 * G.2 * G.1^-1 * G.3^7 ] Genus 13 action of group of order 60 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1, G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 13 action of group of order 144 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^6 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.1 * G.3)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.2 * G.4 * G.2 * G.1 * G.2 * G.1)^2 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 96 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, (G.3 * G.1)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, (G.2 * G.4)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.3 * G.1)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.2 * G.1)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.3 * G.1)^6 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 13 action of group of order 64 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2 * G.3)^2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 13 action of group of order 60 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^3 * G.3 * G.2 * G.4^3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-14 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-10 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 13 action of group of order 56 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.4^-7 ] Genus 13 action of group of order 52 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-6 * G.2 * G.3 * G.4^-6 ] Genus 13 action of group of order 52 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-9 * G.1 * G.3 * G.4^-3 ] Genus 13 action of group of order 52 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-6 * G.1 * G.4^6 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.2 * G.4 * G.3)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2, G.4), G.4^-3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1^-1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.3)^4 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 13 action of group of order 72 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 13 has order 360 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 13 has order 720 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 13 has order 720 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 13 has order 144 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 14 has order 360 ... group action with signature (0; +; [-]; {(2,3,10)}) Check total 320 : 86 chiral, 234 reflexible, with 71 non-orientable quotient actions Genus 14 actions: Genus 14 action of group of order 1092 via triangle group [ 2, 3, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 14 action of group of order 1092 via triangle group [ 2, 3, 7 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 14 action of group of order 1092 via triangle group [ 2, 3, 7 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 14 action of group of order 120 via triangle group [ 2, 4, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-24 * G.1 * G.2 * G.3^-5 ] Genus 14 action of group of order 112 via triangle group [ 2, 4, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-22 * G.1 * G.2^-1 * G.3^-5 ] Genus 14 action of group of order 156 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 14 action of group of order 156 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 14 action of group of order 156 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 14 action of group of order 156 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 14 action of group of order 96 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^5 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^4 ] Genus 14 action of group of order 84 via triangle group [ 2, 6, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 14 action of group of order 80 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-5 ] Genus 14 action of group of order 70 via triangle group [ 2, 10, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-3 * G.1 * G.2^-1 * G.3^-3 ] Genus 14 action of group of order 58 via triangle group [ 2, 29, 58 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^18 * G.2^-10 ] Genus 14 action of group of order 60 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^18 * G.2^-11 ] Genus 14 action of group of order 56 via triangle group [ 2, 56, 56 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^17 * G.2^-10 ] Genus 14 action of group of order 120 via triangle group [ 3, 4, 5 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 14 action of group of order 78 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 14 action of group of order 78 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 14 action of group of order 78 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 14 action of group of order 78 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 ] Genus 14 action of group of order 60 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1 * G.3 ] Genus 14 action of group of order 60 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 ] Genus 14 action of group of order 60 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 14 action of group of order 56 via triangle group [ 4, 4, 28 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^6 * G.2^-1 * G.1 * G.3^7 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-7 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-10 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 14 action of group of order 60 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 14 action of group of order 56 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-7 * G.1 * G.4^-7 ] Genus 14 action of group of order 56 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-10 * G.2 * G.4^-4 ] Genus 14 action of group of order 56 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-5 * G.1 * G.2 * G.1^2 * G.4^-8 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 ] Genus 14 action of group of order 78 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 ] Largest orientation-preserving group for genus 14 has order 1092 ... group action with signature (0: +; [2,3,7]; {-}) Largest group with or without reflections for genus 14 has order 2184 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest group with reflections for genus 14 has order 2184 ... group action with signature (0; +; [-]; {(2,3,7)}) Largest chiral group for genus 14 has order 156 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 15 has order 1092 ... group action with signature (0; +; [-]; {(2,3,7)}) Check total 93 : 56 chiral, 37 reflexible, with 9 non-orientable quotient actions Genus 15 actions: Genus 15 action of group of order 504 via triangle group [ 2, 3, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 15 action of group of order 336 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 15 action of group of order 336 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 15 action of group of order 294 via triangle group [ 2, 3, 14 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^9 * G.2 * G.1 * G.3^-1 * G.1 * G.3^4 ] Genus 15 action of group of order 240 via triangle group [ 2, 3, 20 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3 * G.2^2 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 15 action of group of order 336 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.3 * G.2^-1 * G.3)^3 ] Genus 15 action of group of order 144 via triangle group [ 2, 4, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-5 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 15 action of group of order 128 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-5 * G.1 * G.3^5 * G.2^-1 * G.3^-5 ] Genus 15 action of group of order 128 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-18 * G.1 * G.3^7 * G.2^-1 * G.3^-6 ] Genus 15 action of group of order 120 via triangle group [ 2, 4, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-24 * G.1 * G.2^-1 * G.3^-5 ] Genus 15 action of group of order 120 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.2^-2 * G.3^-3 ] Genus 15 action of group of order 98 via triangle group [ 2, 7, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-7 ] Genus 15 action of group of order 96 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 15 action of group of order 96 via triangle group [ 2, 8, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 15 action of group of order 96 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^6 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 15 action of group of order 96 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 15 action of group of order 80 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-5 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 15 action of group of order 80 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^5 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 15 action of group of order 70 via triangle group [ 2, 14, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-2 * G.3^3 ] Genus 15 action of group of order 72 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-14 * G.3 * G.2^-1 ] Genus 15 action of group of order 66 via triangle group [ 2, 22, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-2 * G.3^2 * G.2^-6 * G.3 ] Genus 15 action of group of order 62 via triangle group [ 2, 31, 62 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^19 * G.2^-10 * G.3 ] Genus 15 action of group of order 64 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^20 * G.2^-11 ] Genus 15 action of group of order 64 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2^8 * G.3^-2 * G.2^3 * G.3^-1 ] Genus 15 action of group of order 60 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^18 * G.2^-10 * G.3 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 15 action of group of order 168 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 15 action of group of order 147 via triangle group [ 3, 3, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 15 action of group of order 120 via triangle group [ 3, 3, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-2 * G.1 * G.3^2, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 15 action of group of order 93 via triangle group [ 3, 3, 31 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 15 action of group of order 93 via triangle group [ 3, 3, 31 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 15 action of group of order 168 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 15 action of group of order 96 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 15 action of group of order 96 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3 ] Genus 15 action of group of order 96 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 15 action of group of order 84 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 15 action of group of order 84 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 15 action of group of order 72 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-5 * G.1 * G.2 * G.3^-3 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-4 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 15 action of group of order 64 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-16 ] Genus 15 action of group of order 60 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-8 * G.1 * G.2^-1 * G.3^-6 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 112 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 15 action of group of order 84 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1^2 * G.4^4 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^3 * G.3 * G.4^-2 * G.1 * G.2 * G.4^3 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^9 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^-5 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 15 action of group of order 72 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^9 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-16 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-11 * G.1^2 * G.4^-5 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^7 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.1 * G.4^-4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.3 * G.1 * G.4^-4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 64 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-7 * G.2 * G.3 * G.4^-7 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-10 * G.2 * G.1^2 * G.4^-5 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^7 * G.2 * G.1 * G.4^7 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-5, G.4 * G.3^-1 * G.4 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.4 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.1)^3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1, G.4 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.4^-1)^2, G.3^-1 * G.4^-1 * G.2 * G.4^2 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.3 * G.4^-1)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, (G.3^-1 * G.1)^3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4 * G.3 * G.1 * G.4 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.2 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.2, G.3^-1 * G.4^-1 * G.1 * G.4^2 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1)^2, G.4^-5, G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.3 * G.2^-1)^3, G.2^-1 * G.4 * G.3 * G.1 * G.4^2, (G.4^-1 * G.2^-1)^3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4, G.4^-5, G.4^-2 * G.2 * G.3 * G.2^-1 * G.4^-2 * G.2^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.3 * G.2^-1)^3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.1 * G.4)^2, (G.1 * G.2^-1)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2, (G.4^-1 * G.2^-1)^3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2^-1 * G.4^2, G.4^2 * G.2^-1 * G.4^-1 * G.1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.3 * G.2^-1 * G.4^2 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.1 * G.4)^2, (G.1 * G.2^-1)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4^-1 * G.1 * G.2^-1 * G.4^-1, G.4 * G.1 * G.2 * G.3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.1 * G.2^-1 * G.4^2, G.3 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2^-1 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-5, G.4^-2 * G.2^-1 * G.1 * G.2 * G.4^-2 * G.2^-1 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-5, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^2 * G.3 ] Genus 15 action of group of order 60 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.4^-1 ] Largest orientation-preserving group for genus 15 has order 504 ... group action with signature (0: +; [2,3,9]; {-}) Largest group with or without reflections for genus 15 has order 1008 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest group with reflections for genus 15 has order 1008 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest chiral group for genus 15 has order 336 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 16 has order 504 ... group action with signature (0; +; [-]; {(2,3,9)}) Check total 159 : 72 chiral, 87 reflexible, with 33 non-orientable quotient actions Genus 16 actions: Genus 16 action of group of order 720 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 16 action of group of order 600 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 16 action of group of order 200 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^10 ] Genus 16 action of group of order 136 via triangle group [ 2, 4, 34 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-27 * G.1 * G.2 * G.3^-6 ] Genus 16 action of group of order 128 via triangle group [ 2, 4, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-25 * G.1 * G.2^-1 * G.3^-6 ] Genus 16 action of group of order 300 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 16 action of group of order 144 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^8 ] Genus 16 action of group of order 108 via triangle group [ 2, 6, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^6 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 16 action of group of order 108 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.1 * G.3^11 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 16 action of group of order 108 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 16 action of group of order 108 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 16 action of group of order 96 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.1 * G.3^10 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 16 action of group of order 100 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-10, G.3^2 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 16 action of group of order 100 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^10, (G.2 * G.3^-1 * G.2^3)^2 ] Genus 16 action of group of order 100 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 16 action of group of order 80 via triangle group [ 2, 10, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^10 ] Genus 16 action of group of order 72 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.2^8 * G.3^-2 * G.2^6 ] Genus 16 action of group of order 66 via triangle group [ 2, 33, 66 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^21 * G.2^-10 * G.3 ] Genus 16 action of group of order 68 via triangle group [ 2, 34, 34 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^22 * G.2^-11 ] Genus 16 action of group of order 64 via triangle group [ 2, 64, 64 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^20 * G.2^-10 * G.3 ] Genus 16 action of group of order 360 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 16 action of group of order 120 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.3^6 ] Genus 16 action of group of order 120 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2 ] Genus 16 action of group of order 72 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 16 action of group of order 72 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 16 action of group of order 72 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3 * G.2 * G.1^-1 * G.3^2, G.2^6 ] Genus 16 action of group of order 72 via triangle group [ 3, 8, 8 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.2^-2, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8 ] Genus 16 action of group of order 72 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.2^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^8 ] Genus 16 action of group of order 72 via triangle group [ 3, 8, 8 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8 ] Genus 16 action of group of order 100 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 16 action of group of order 100 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 16 action of group of order 100 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 16 action of group of order 68 via triangle group [ 4, 4, 17 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.2 * G.1 * G.3^-2 ] Genus 16 action of group of order 68 via triangle group [ 4, 4, 17 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2 * G.1 * G.3^2 ] Genus 16 action of group of order 68 via triangle group [ 4, 4, 17 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^9 * G.2 * G.1 * G.3^7 ] Genus 16 action of group of order 64 via triangle group [ 4, 4, 32 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-9 * G.1 * G.2^-1 * G.3^-6 ] Genus 16 action of group of order 72 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 16 action of group of order 72 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1 * G.3^-1 * G.1 ] Genus 16 action of group of order 72 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 16 action of group of order 72 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^6 ] Genus 16 action of group of order 72 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, (G.2 * G.1)^5 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.3 * G.1)^3 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 16 action of group of order 120 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 16 action of group of order 100 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 16 action of group of order 100 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 ] Genus 16 action of group of order 100 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 16 action of group of order 68 via quadrangle group [ 2, 2, 2, 17 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-8 * G.2 * G.1 * G.3 * G.4^-8 ] Genus 16 action of group of order 68 via quadrangle group [ 2, 2, 2, 17 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-12 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 16 action of group of order 68 via quadrangle group [ 2, 2, 2, 17 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-8 * G.1^2 * G.4^-9 ] Genus 16 action of group of order 64 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-8 * G.1 * G.4^-8 ] Genus 16 action of group of order 64 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-11 * G.1 * G.3 * G.4^-4 ] Genus 16 action of group of order 64 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^8 * G.2 * G.1 * G.4^7 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2 * G.1 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^2 * G.3 * G.2^-1 * G.4 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2 * G.1 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.4 ] Genus 16 action of group of order 72 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Largest orientation-preserving group for genus 16 has order 720 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 16 has order 1440 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 16 has order 1440 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 16 has order 120 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 17 has order 720 ... group action with signature (0; +; [-]; {(2,3,8)}) Check total 112 : 36 chiral, 76 reflexible, with 31 non-orientable quotient actions Genus 17 actions: Genus 17 action of group of order 1344 via triangle group [ 2, 3, 7 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 17 action of group of order 1344 via triangle group [ 2, 3, 7 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 17 action of group of order 768 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 17 action of group of order 336 via triangle group [ 2, 3, 14 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-3 * G.1 * G.3 ] Genus 17 action of group of order 384 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^4, (G.2^-1 * G.3^2)^4 ] Genus 17 action of group of order 384 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4 ] Genus 17 action of group of order 384 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 17 action of group of order 384 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 17 action of group of order 384 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 17 action of group of order 256 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 17 action of group of order 256 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 17 action of group of order 256 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 17 action of group of order 256 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 17 action of group of order 192 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 17 action of group of order 192 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 17 action of group of order 192 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-12 ] Genus 17 action of group of order 160 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-14 * G.1 * G.2 * G.3^-5 ] Genus 17 action of group of order 144 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-29 * G.1 * G.2 * G.3^-6 ] Genus 17 action of group of order 136 via triangle group [ 2, 4, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-27 * G.1 * G.2^-1 * G.3^-6 ] Genus 17 action of group of order 240 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 17 action of group of order 160 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.2 * G.1 * G.3 * G.2^2 * G.3^-3 ] Genus 17 action of group of order 160 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 17 action of group of order 192 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 17 action of group of order 120 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 17 action of group of order 102 via triangle group [ 2, 6, 51 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-1 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 17 action of group of order 112 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.2^-1 * G.3 * G.2^-2 * G.3^3 ] Genus 17 action of group of order 112 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, (G.2 * G.3^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, (G.2 * G.3^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 128 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 96 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 17 action of group of order 96 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-7 ] Genus 17 action of group of order 96 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2 ] Genus 17 action of group of order 96 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-12 ] Genus 17 action of group of order 96 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-12 ] Genus 17 action of group of order 80 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-1 * G.2^8)^2 ] Genus 17 action of group of order 70 via triangle group [ 2, 35, 70 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^23 * G.2^-10 * G.3 ] Genus 17 action of group of order 72 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^24 * G.2^-11 ] Genus 17 action of group of order 68 via triangle group [ 2, 68, 68 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^22 * G.2^-10 * G.3 ] Genus 17 action of group of order 384 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 17 action of group of order 168 via triangle group [ 3, 3, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 17 action of group of order 168 via triangle group [ 3, 3, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 17 action of group of order 168 via triangle group [ 3, 3, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 17 action of group of order 168 via triangle group [ 3, 3, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 17 action of group of order 168 via triangle group [ 3, 3, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 17 action of group of order 96 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 17 action of group of order 120 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 17 action of group of order 96 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 17 action of group of order 96 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, (G.1 * G.3 * G.2)^2 ] Genus 17 action of group of order 96 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, (G.2^-1 * G.3)^4 ] Genus 17 action of group of order 96 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-1 * G.1^-1 * G.2^-2 * G.3^-1 ] Genus 17 action of group of order 96 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-1)^4 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 ] Genus 17 action of group of order 128 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^6 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^6 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^6 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 17 action of group of order 96 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^6 ] Genus 17 action of group of order 80 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^10 ] Genus 17 action of group of order 80 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 17 action of group of order 80 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 17 action of group of order 72 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^9 * G.2^-1 * G.1^-1 * G.3^8 ] Genus 17 action of group of order 68 via triangle group [ 4, 4, 34 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^9 * G.2 * G.1^-1 * G.3^7 ] Genus 17 action of group of order 80 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.3^-1)^2, G.1^-5, (G.1 * G.2^-2)^2, G.2^-5 ] Genus 17 action of group of order 80 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.2^-1)^2, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2 ] Genus 17 action of group of order 80 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^-5 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 192 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^8 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 128 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.1^2 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-5 * G.1^2 * G.4^-5 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^6 * G.1^2 * G.4^4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^10 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^5 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.1^2 * G.4^3 ] Genus 17 action of group of order 80 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^4 * G.3 * G.2 * G.4^4 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.1 * G.4^3 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^4 * G.2 * G.1 * G.4^4 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-3 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-18 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-13 * G.1^2 * G.4^-5 ] Genus 17 action of group of order 72 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-9 ] Genus 17 action of group of order 68 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-8 * G.2 * G.3 * G.4^-8 ] Genus 17 action of group of order 68 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-12 * G.2 * G.1^2 * G.4^-5 ] Genus 17 action of group of order 68 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-7 * G.1 * G.2 * G.1^2 * G.4^-9 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.3^-1 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3 * G.1 * G.3^-1 * G.1)^4, G.2 * G.1^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^8, G.2 * G.1^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, (G.1 * G.2)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.3 * G.4^-1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.1)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.1 * G.2^-1)^3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.1 * G.2^-1)^3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.2^-1 * G.4^-1)^4, G.3 * G.1^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.3)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.3 * G.1)^2 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.2^-1 * G.3 * G.1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.1)^4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-1)^4, G.3 * G.1^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 17 action of group of order 96 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Largest orientation-preserving group for genus 17 has order 1344 ... group action with signature (0: +; [2,3,7]; {-}) Largest group with or without reflections for genus 17 has order 1536 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 17 has order 1536 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 17 has order 1344 ... group action with signature (0: +; [2,3,7]; {-}) Largest non-orientable group for non-orientable genus 18 has order 192 ... group action with signature (0; +; [-]; {(2,2,2,3)}) Check total 462 : 164 chiral, 298 reflexible, with 56 non-orientable quotient actions Genus 18 actions: Genus 18 action of group of order 168 via triangle group [ 2, 4, 21 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-8 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 18 action of group of order 152 via triangle group [ 2, 4, 38 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-31 * G.1 * G.2 * G.3^-6 ] Genus 18 action of group of order 144 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-29 * G.1 * G.2^-1 * G.3^-6 ] Genus 18 action of group of order 120 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^7 * G.2^-1 * G.1 * G.3^12 ] Genus 18 action of group of order 136 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 ] Genus 18 action of group of order 136 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 ] Genus 18 action of group of order 136 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-3 ] Genus 18 action of group of order 136 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-4 * G.3^-1 * G.1 * G.3 ] Genus 18 action of group of order 112 via triangle group [ 2, 8, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-4 * G.1 * G.3^3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 18 action of group of order 90 via triangle group [ 2, 10, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 ] Genus 18 action of group of order 96 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 18 action of group of order 84 via triangle group [ 2, 14, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-4 * G.3 * G.2^-7 * G.3 * G.2^-1 ] Genus 18 action of group of order 80 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^6 * G.3^-4 ] Genus 18 action of group of order 84 via triangle group [ 2, 21, 21 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-10 * G.2^8 * G.3^-1 ] Genus 18 action of group of order 78 via triangle group [ 2, 26, 39 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-3 * G.3^2 * G.2^-6 * G.3 * G.2^-1 ] Genus 18 action of group of order 74 via triangle group [ 2, 37, 74 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^25 * G.2^-10 * G.3 ] Genus 18 action of group of order 76 via triangle group [ 2, 38, 38 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^38 ] Genus 18 action of group of order 72 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^24 * G.2^-10 * G.3 ] Genus 18 action of group of order 111 via triangle group [ 3, 3, 37 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 ] Genus 18 action of group of order 111 via triangle group [ 3, 3, 37 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 18 action of group of order 76 via triangle group [ 4, 4, 19 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^10 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^4 ] Genus 18 action of group of order 72 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^9 * G.2^-1 * G.1 * G.3^8 ] Genus 18 action of group of order 76 via quadrangle group [ 2, 2, 2, 19 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-9 * G.2 * G.1 * G.3 * G.4^-9 ] Genus 18 action of group of order 76 via quadrangle group [ 2, 2, 2, 19 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-14 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 18 action of group of order 76 via quadrangle group [ 2, 2, 2, 19 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-19 ] Genus 18 action of group of order 72 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-9 * G.1 * G.4^-9 ] Genus 18 action of group of order 72 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-13 * G.1 * G.3 * G.4^-4 ] Genus 18 action of group of order 72 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-4 * G.1 * G.4^3 * G.2 * G.1^2 * G.4^-10 ] Largest orientation-preserving group for genus 18 has order 168 ... group action with signature (0: +; [2,4,21]; {-}) Largest group with or without reflections for genus 18 has order 336 ... group action with signature (0; +; [-]; {(2,4,21)}) Largest group with reflections for genus 18 has order 336 ... group action with signature (0; +; [-]; {(2,4,21)}) Largest chiral group for genus 18 has order 136 ... group action with signature (0: +; [2,8,8]; {-}) Largest non-orientable group for non-orientable genus 19 has order 168 ... group action with signature (0; +; [-]; {(2,4,21)}) Check total 28 : 4 chiral, 24 reflexible, with 6 non-orientable quotient actions Genus 19 actions: Genus 19 action of group of order 432 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 19 action of group of order 288 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.3^-5 ] Genus 19 action of group of order 720 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 19 action of group of order 336 via triangle group [ 2, 4, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 19 action of group of order 288 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 19 action of group of order 288 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, (G.2^-1 * G.3)^6 ] Genus 19 action of group of order 288 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 19 action of group of order 288 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 19 action of group of order 240 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 19 action of group of order 216 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 19 action of group of order 216 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 160 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-14 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 19 action of group of order 160 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-33 * G.1 * G.2 * G.3^-6 ] Genus 19 action of group of order 152 via triangle group [ 2, 4, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-31 * G.1 * G.2^-1 * G.3^-6 ] Genus 19 action of group of order 360 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^4 ] Genus 19 action of group of order 162 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 162 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, (G.2^-2 * G.3)^3 ] Genus 19 action of group of order 162 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 19 action of group of order 162 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.2^-2 * G.3)^3 ] Genus 19 action of group of order 144 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.1 * G.3^2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 19 action of group of order 144 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 19 action of group of order 144 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1)^4 ] Genus 19 action of group of order 126 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-13 ] Genus 19 action of group of order 114 via triangle group [ 2, 6, 57 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-13 ] Genus 19 action of group of order 168 via triangle group [ 2, 7, 7 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.2 * G.3^-1 * G.2^3 * G.3^-3 ] Genus 19 action of group of order 144 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^-2 * G.2^3 * G.3^-1 * G.2 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 120 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 108 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-3 * G.3^-3 ] Genus 19 action of group of order 108 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^4 * G.3^-3 ] Genus 19 action of group of order 96 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12 ] Genus 19 action of group of order 96 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-2 * G.3^2 * G.2^-5 * G.3^2 * G.2^-1 ] Genus 19 action of group of order 90 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-9 ] Genus 19 action of group of order 78 via triangle group [ 2, 39, 78 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^39 ] Genus 19 action of group of order 80 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^40 ] Genus 19 action of group of order 80 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2^10 * G.3^-1 * G.2^8 ] Genus 19 action of group of order 76 via triangle group [ 2, 76, 76 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^37 * G.3^-1 ] Genus 19 action of group of order 216 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 19 action of group of order 216 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 216 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 216 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 19 action of group of order 216 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 19 action of group of order 144 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 19 action of group of order 117 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 19 action of group of order 117 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 19 action of group of order 144 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 19 action of group of order 108 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 19 action of group of order 108 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 108 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 19 action of group of order 108 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 19 action of group of order 120 via triangle group [ 3, 5, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 19 action of group of order 78 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 78 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.3 * G.2^-2)^3 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.2^3 * G.3^-2 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 19 action of group of order 81 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^-1 * G.2^3 * G.3^-2, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2^-2 * G.1 * G.3^2 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^2 * G.3 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.2 ] Genus 19 action of group of order 144 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 19 action of group of order 120 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2 ] Genus 19 action of group of order 108 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.2^-1 * G.1)^3 ] Genus 19 action of group of order 108 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.2^-1 * G.1)^3 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-10 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.2^-1 * G.3 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 ] Genus 19 action of group of order 80 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 ] Genus 19 action of group of order 76 via triangle group [ 4, 4, 38 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^10 * G.2^-1 * G.1 * G.3^8 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^9 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.1 * G.3)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^9 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.3 * G.1)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 144 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-5, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^-5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^-5, (G.1 * G.2)^4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-5 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 19 action of group of order 120 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^6 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^9 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.3 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.3 * G.1)^6 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.4^2 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.3 * G.1)^6 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 108 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.3 * G.1)^6 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-2 * G.1 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.1^2 * G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.1^2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.1^2 * G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.1^2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.1 * G.3 * G.2 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.3 * G.1)^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.2 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.3 * G.1 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.4^2 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 19 action of group of order 96 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, (G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.1 * G.4^3 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 19 action of group of order 84 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-20 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-15 * G.1^2 * G.4^-5 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-11 * G.1^2 * G.4^-9 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-5 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^5 * G.3 * G.1 * G.2 * G.4^4 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^5 * G.2 * G.4 * G.2 * G.4^4 ] Genus 19 action of group of order 80 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 19 action of group of order 76 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-9 * G.2 * G.3 * G.4^-9 ] Genus 19 action of group of order 76 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-14 * G.2 * G.1^2 * G.4^-5 ] Genus 19 action of group of order 76 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-11 * G.1 * G.2 * G.4^-7 ] Largest orientation-preserving group for genus 19 has order 720 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 19 has order 1440 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 19 has order 1440 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 19 has order 288 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 20 has order 240 ... group action with signature (0; +; [-]; {(2,4,10)}) Check total 429 : 196 chiral, 233 reflexible, with 85 non-orientable quotient actions Genus 20 actions: Genus 20 action of group of order 168 via triangle group [ 2, 4, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-35 * G.1 * G.2 * G.3^-6 ] Genus 20 action of group of order 160 via triangle group [ 2, 4, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-33 * G.1 * G.2^-1 * G.3^-6 ] Genus 20 action of group of order 228 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 20 action of group of order 228 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 20 action of group of order 228 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 20 action of group of order 228 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 20 action of group of order 132 via triangle group [ 2, 6, 22 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-8 * G.1 * G.2 * G.3^-13 ] Genus 20 action of group of order 120 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-12 * G.1 ] Genus 20 action of group of order 144 via triangle group [ 2, 8, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 20 action of group of order 112 via triangle group [ 2, 8, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-4 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 20 action of group of order 120 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-6 * G.1 * G.2 * G.3^-5 ] Genus 20 action of group of order 96 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 20 action of group of order 90 via triangle group [ 2, 18, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2^-4 * G.3^4 ] Genus 20 action of group of order 88 via triangle group [ 2, 22, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-5 * G.2^9 * G.3^-2 * G.2^5 * G.3^-1 ] Genus 20 action of group of order 82 via triangle group [ 2, 41, 82 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^41 ] Genus 20 action of group of order 84 via triangle group [ 2, 42, 42 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^42 ] Genus 20 action of group of order 80 via triangle group [ 2, 80, 80 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^39 * G.3^-1 ] Genus 20 action of group of order 120 via triangle group [ 3, 4, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^2 ] Genus 20 action of group of order 114 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 20 action of group of order 114 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 20 action of group of order 114 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 20 action of group of order 114 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 20 action of group of order 84 via triangle group [ 4, 4, 21 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-14 * G.1 * G.2 * G.3^-6 ] Genus 20 action of group of order 80 via triangle group [ 4, 4, 40 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-10 * G.1 * G.2^-1 * G.3^-9 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-10 * G.2 * G.1 * G.3 * G.4^-10 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-16 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 20 action of group of order 84 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-11 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Genus 20 action of group of order 80 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-10 * G.1 * G.4^-10 ] Genus 20 action of group of order 80 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-15 * G.1 * G.3 * G.4^-4 ] Genus 20 action of group of order 80 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-11 * G.1 * G.2 * G.4^-8 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 20 action of group of order 114 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Largest orientation-preserving group for genus 20 has order 228 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 20 has order 336 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest group with reflections for genus 20 has order 336 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest chiral group for genus 20 has order 228 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 21 has order 132 ... group action with signature (0; +; [-]; {(2,6,22)}) Check total 116 : 80 chiral, 36 reflexible, with 9 non-orientable quotient actions Genus 21 actions: Genus 21 action of group of order 384 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-10 * G.1 * G.2 * G.3^-5 ] Genus 21 action of group of order 384 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3, G.3^-1 * G.1 * G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-5 ] Genus 21 action of group of order 480 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^5 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.3^-1 * G.2)^5 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 21 action of group of order 320 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 21 action of group of order 240 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-12 ] Genus 21 action of group of order 240 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-12 ] Genus 21 action of group of order 240 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 240 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 200 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 21 action of group of order 200 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-11 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-18 * G.1 * G.2 * G.3^-5 ] Genus 21 action of group of order 192 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 21 action of group of order 176 via triangle group [ 2, 4, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-37 * G.1 * G.2 * G.3^-6 ] Genus 21 action of group of order 168 via triangle group [ 2, 4, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-35 * G.1 * G.2^-1 * G.3^-6 ] Genus 21 action of group of order 240 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-2 * G.2)^2 ] Genus 21 action of group of order 192 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 21 action of group of order 192 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 192 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^8 ] Genus 21 action of group of order 192 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^8 ] Genus 21 action of group of order 192 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2 ] Genus 21 action of group of order 160 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 21 action of group of order 160 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 160 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 160 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.2^2 * G.3^-1 * G.2^2 * G.3^-3 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^8 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^11 * G.2^-1 * G.3^-3 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-10 * G.1 * G.2 * G.3^-5 ] Genus 21 action of group of order 128 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 112 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-5 ] Genus 21 action of group of order 112 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^8 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 120 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2^7 * G.3^-1 * G.2^2 ] Genus 21 action of group of order 120 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2^7 * G.3^-1 * G.2^2 ] Genus 21 action of group of order 112 via triangle group [ 2, 14, 14 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^-14 ] Genus 21 action of group of order 112 via triangle group [ 2, 14, 14 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^-3 * G.3 * G.2^-8 * G.3^2 ] Genus 21 action of group of order 96 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-3 * G.2^2 * G.3^-3 ] Genus 21 action of group of order 96 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-6 * G.3^2 * G.2^-5 * G.3^2 * G.2^-1 ] Genus 21 action of group of order 100 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^6 * G.3^-2 * G.2 * G.3^-1 ] Genus 21 action of group of order 100 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^6 * G.3^-1 * G.2 * G.3^-2 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-13 * G.2^8 * G.3^-1 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-3 * G.3^-1 * G.2^2 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^3 * G.3^-2 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-5 * G.2^9 * G.3^-2 * G.2^5 * G.3^-1 * G.2 ] Genus 21 action of group of order 96 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-9 * G.3 * G.2^-1 * G.3 ] Genus 21 action of group of order 86 via triangle group [ 2, 43, 86 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^43 ] Genus 21 action of group of order 88 via triangle group [ 2, 44, 44 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^44 ] Genus 21 action of group of order 84 via triangle group [ 2, 84, 84 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^41 * G.3^-1 ] Genus 21 action of group of order 192 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^8 ] Genus 21 action of group of order 192 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3^8, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1 ] Genus 21 action of group of order 129 via triangle group [ 3, 3, 43 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2 * G.1 * G.3^3 ] Genus 21 action of group of order 129 via triangle group [ 3, 3, 43 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 240 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2 ] Genus 21 action of group of order 120 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^8 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.2)^3, G.2^8 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, (G.2 * G.3^-1 * G.2)^2, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^3 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, (G.1^-1 * G.3 * G.2)^2, G.2^8 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 160 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 21 action of group of order 120 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 ] Genus 21 action of group of order 120 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 ] Genus 21 action of group of order 100 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 100 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-2 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.2^-1 * G.1)^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-5 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.2^-1 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^-3 * G.1^-1 * G.2 * G.3^-2 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^2 * G.2 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^2 * G.2 * G.1^-1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-4 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8 * G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 21 action of group of order 96 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-5 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 21 action of group of order 88 via triangle group [ 4, 4, 22 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-22 ] Genus 21 action of group of order 84 via triangle group [ 4, 4, 42 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-14 * G.1 * G.2^-1 * G.3^-6 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, (G.2^-1 * G.1)^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.2^-2, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 21 action of group of order 96 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 21 action of group of order 240 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^10 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^10 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.2 * G.1)^5 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 21 action of group of order 160 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.2 * G.1)^5 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, (G.4^-1 * G.2)^5 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.3 * G.1)^5 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.1)^5 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.1)^5 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 21 action of group of order 100 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-12 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-12 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.3 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-6 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-8 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^12 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-12 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-5 * G.2 * G.1 * G.4^4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.4^-4 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-6 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^12 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1^2 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1^2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-4 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^6 * G.3 * G.2 * G.4^4 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.4^-3 * G.1 * G.4 * G.1^2 * G.4^3 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.3 * G.1 * G.4^3 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.4^4 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^-2 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-22 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-17 * G.1^2 * G.4^-5 ] Genus 21 action of group of order 88 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^12 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 21 action of group of order 84 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-10 * G.2 * G.3 * G.4^-10 ] Genus 21 action of group of order 84 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-16 * G.2 * G.1^2 * G.4^-5 ] Genus 21 action of group of order 84 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-7 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.2)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.2)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, (G.1 * G.3^-1)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3^-1 * G.4 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.4^-1 * G.3)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.3 * G.1)^2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.3 * G.1)^2 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1 * G.2^-1 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 21 action of group of order 120 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1 * G.3 * G.1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.1 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.1 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.1 * G.2^-1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.2^-1 * G.4 * G.3)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.3 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.3 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, (G.2^-1 * G.3)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.2^-1 * G.1)^4 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.2 * G.4^-1 * G.1)^2 ] Genus 21 action of group of order 96 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.2 * G.4^-1 * G.1)^2 ] Largest orientation-preserving group for genus 21 has order 480 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 21 has order 960 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 21 has order 960 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 21 has order 320 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 22 has order 240 ... group action with signature (0; +; [-]; {(2,2,2,3)}) ... group action with signature (0; +; [-]; {(2,6,6)}) Check total 532 : 236 chiral, 296 reflexible, with 100 non-orientable quotient actions Genus 22 actions: Genus 22 action of group of order 1008 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 22 action of group of order 1008 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 22 action of group of order 504 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 22 action of group of order 504 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 22 action of group of order 336 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 ] Genus 22 action of group of order 336 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3 * G.2^-1 * G.3)^3 ] Genus 22 action of group of order 184 via triangle group [ 2, 4, 46 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-39 * G.1 * G.2 * G.3^-6 ] Genus 22 action of group of order 176 via triangle group [ 2, 4, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-37 * G.1 * G.2^-1 * G.3^-6 ] Genus 22 action of group of order 240 via triangle group [ 2, 5, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 22 action of group of order 252 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 22 action of group of order 168 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 22 action of group of order 168 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 22 action of group of order 168 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 22 action of group of order 168 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 22 action of group of order 144 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 22 action of group of order 144 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-2 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-14 ] Genus 22 action of group of order 144 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-10 * G.1 * G.2 * G.3^-13 ] Genus 22 action of group of order 144 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 22 action of group of order 132 via triangle group [ 2, 6, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-13 * G.1 ] Genus 22 action of group of order 144 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^-1 * G.1 * G.2^-3 * G.3^-4 ] Genus 22 action of group of order 126 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-9 ] Genus 22 action of group of order 126 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-9 ] Genus 22 action of group of order 110 via triangle group [ 2, 10, 55 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 22 action of group of order 108 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.2^-6 * G.3^3)^2 ] Genus 22 action of group of order 108 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^7 * G.2^-8 * G.3 * G.2^-2 ] Genus 22 action of group of order 90 via triangle group [ 2, 45, 90 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^45 ] Genus 22 action of group of order 92 via triangle group [ 2, 46, 46 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^46 ] Genus 22 action of group of order 88 via triangle group [ 2, 88, 88 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^43 * G.3^-1 ] Genus 22 action of group of order 504 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 ] Genus 22 action of group of order 504 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 22 action of group of order 252 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 22 action of group of order 252 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-2 * G.2^2 * G.3^-1 * G.2 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 22 action of group of order 126 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 22 action of group of order 168 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 22 action of group of order 168 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, (G.3^-1 * G.1)^3 ] Genus 22 action of group of order 92 via triangle group [ 4, 4, 23 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 * G.1 * G.2 * G.3^-7 ] Genus 22 action of group of order 88 via triangle group [ 4, 4, 44 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 * G.1 * G.2^-1 * G.3^-6 ] Genus 22 action of group of order 120 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.2)^3 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 22 action of group of order 168 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-2 * G.1 * G.2 * G.4^4 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^5 * G.1^2 * G.4^4 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^5 * G.1^2 * G.4^4 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^5 * G.1^2 * G.4^4 ] Genus 22 action of group of order 108 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^5 * G.1^2 * G.4^4 ] Genus 22 action of group of order 92 via quadrangle group [ 2, 2, 2, 23 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-11 * G.2 * G.1 * G.3 * G.4^-11 ] Genus 22 action of group of order 92 via quadrangle group [ 2, 2, 2, 23 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-23 ] Genus 22 action of group of order 92 via quadrangle group [ 2, 2, 2, 23 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-13 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Genus 22 action of group of order 88 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-11 * G.1 * G.4^-11 ] Genus 22 action of group of order 88 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-17 * G.1 * G.3 * G.4^-4 ] Genus 22 action of group of order 88 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^13 * G.2 * G.1 * G.4^8 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 22 action of group of order 126 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Largest orientation-preserving group for genus 22 has order 1008 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 22 has order 2016 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 22 has order 2016 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 22 has order 504 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 23 has order 1008 ... group action with signature (0; +; [-]; {(2,3,8)}) Check total 228 : 166 chiral, 62 reflexible, with 16 non-orientable quotient actions Genus 23 actions: Genus 23 action of group of order 192 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-18 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 23 action of group of order 192 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2 * G.3^-6 ] Genus 23 action of group of order 184 via triangle group [ 2, 4, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-39 * G.1 * G.2^-1 * G.3^-6 ] Genus 23 action of group of order 138 via triangle group [ 2, 6, 69 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^9 * G.2^-1 * G.3^-13 * G.1 ] Genus 23 action of group of order 128 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^9 * G.2^-1 * G.3^-5 ] Genus 23 action of group of order 128 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-1 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 23 action of group of order 120 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 23 action of group of order 94 via triangle group [ 2, 47, 94 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^47 ] Genus 23 action of group of order 96 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^48 ] Genus 23 action of group of order 96 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-5 * G.2^9 * G.3^-2 * G.2^6 * G.3^-1 ] Genus 23 action of group of order 92 via triangle group [ 2, 92, 92 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^45 * G.3^-1 ] Genus 23 action of group of order 120 via triangle group [ 3, 5, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^-5 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-18 * G.1^-1 * G.2^-1 * G.3^-5 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-5 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-4 * G.1^-1 * G.3^2 * G.2 * G.3^-5 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 23 action of group of order 96 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-5 * G.1 * G.3^2 * G.2 * G.3^-4 ] Genus 23 action of group of order 92 via triangle group [ 4, 4, 46 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 * G.1 * G.2^-1 * G.3^-7 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3 * G.2^2 * G.1 * G.3^2 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6 ] Genus 23 action of group of order 96 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 176 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 23 action of group of order 132 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-24 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-19 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-14 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.1 * G.4^-5 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4^-1 * G.1 * G.4^-5 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 23 action of group of order 96 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 23 action of group of order 92 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-11 * G.2 * G.3 * G.4^-11 ] Genus 23 action of group of order 92 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-18 * G.1 * G.3 * G.4^-4 ] Genus 23 action of group of order 92 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-12 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Largest orientation-preserving group for genus 23 has order 192 ... group action with signature (0: +; [2,4,48]; {-}) Largest group with or without reflections for genus 23 has order 384 ... group action with signature (0; +; [-]; {(2,4,48)}) Largest group with reflections for genus 23 has order 384 ... group action with signature (0; +; [-]; {(2,4,48)}) Largest chiral group for genus 23 has order 176 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 24 has order 176 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 150 : 64 chiral, 86 reflexible, with 30 non-orientable quotient actions Genus 24 actions: Genus 24 action of group of order 216 via triangle group [ 2, 4, 27 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-14 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 24 action of group of order 200 via triangle group [ 2, 4, 50 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-43 * G.1 * G.2 * G.3^-6 ] Genus 24 action of group of order 192 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2^-1 * G.3^-6 ] Genus 24 action of group of order 156 via triangle group [ 2, 6, 26 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-7 * G.1 * G.3^5 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-7 ] Genus 24 action of group of order 144 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-18 ] Genus 24 action of group of order 144 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^5 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 24 action of group of order 140 via triangle group [ 2, 10, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-14 ] Genus 24 action of group of order 120 via triangle group [ 2, 10, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-5 * G.1 * G.3 * G.2 * G.3^-5 ] Genus 24 action of group of order 120 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 24 action of group of order 112 via triangle group [ 2, 14, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-3 * G.3^3 * G.2^-5 * G.3^3 ] Genus 24 action of group of order 120 via triangle group [ 2, 15, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 24 action of group of order 104 via triangle group [ 2, 26, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-4 * G.2^11 * G.3^-1 * G.2^9 * G.3^-1 ] Genus 24 action of group of order 108 via triangle group [ 2, 27, 27 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-23 * G.3 * G.2^-1 ] Genus 24 action of group of order 102 via triangle group [ 2, 34, 51 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-5 * G.3^3 * G.2^-9 ] Genus 24 action of group of order 98 via triangle group [ 2, 49, 98 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^49 ] Genus 24 action of group of order 100 via triangle group [ 2, 50, 50 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^50 ] Genus 24 action of group of order 96 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^47 * G.3^-1 ] Genus 24 action of group of order 156 via triangle group [ 3, 3, 26 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 24 action of group of order 156 via triangle group [ 3, 3, 26 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 24 action of group of order 147 via triangle group [ 3, 3, 49 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 24 action of group of order 147 via triangle group [ 3, 3, 49 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 24 action of group of order 168 via triangle group [ 3, 4, 7 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 24 action of group of order 168 via triangle group [ 3, 4, 7 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2 ] Genus 24 action of group of order 100 via triangle group [ 4, 4, 25 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^-3 ] Genus 24 action of group of order 100 via triangle group [ 4, 4, 25 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 24 action of group of order 100 via triangle group [ 4, 4, 25 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-19 * G.1^-1 * G.2^-1 * G.3^-5 ] Genus 24 action of group of order 96 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-18 * G.1^-1 * G.2 * G.3^-5 ] Genus 24 action of group of order 120 via triangle group [ 4, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^-5, (G.1 * G.3 * G.2)^2 ] Genus 24 action of group of order 120 via triangle group [ 4, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^-5, (G.2 * G.3^-2)^2 ] Genus 24 action of group of order 120 via triangle group [ 4, 5, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^-5 ] Genus 24 action of group of order 100 via quadrangle group [ 2, 2, 2, 25 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-12 * G.2 * G.1 * G.3 * G.4^-12 ] Genus 24 action of group of order 100 via quadrangle group [ 2, 2, 2, 25 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-25 ] Genus 24 action of group of order 100 via quadrangle group [ 2, 2, 2, 25 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^13 * G.2 * G.1 * G.2 * G.1 * G.4^10 ] Genus 24 action of group of order 96 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-12 * G.1 * G.4^-12 ] Genus 24 action of group of order 96 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-19 * G.2 * G.4^-5 ] Genus 24 action of group of order 96 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-13 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Largest orientation-preserving group for genus 24 has order 216 ... group action with signature (0: +; [2,4,27]; {-}) Largest group with or without reflections for genus 24 has order 432 ... group action with signature (0; +; [-]; {(2,4,27)}) Largest group with reflections for genus 24 has order 432 ... group action with signature (0; +; [-]; {(2,4,27)}) No chiral group action for genus 24 Largest non-orientable group for non-orientable genus 25 has order 216 ... group action with signature (0; +; [-]; {(2,4,27)}) Check total 36 : 0 chiral, 36 reflexible, with 12 non-orientable quotient actions Genus 25 actions: Genus 25 action of group of order 720 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^4 ] Genus 25 action of group of order 576 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 576 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 25 action of group of order 384 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^3 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-1 * G.1 * G.3^3, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^-3 * G.1 * G.3 ] Genus 25 action of group of order 360 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 320 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 320 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2, G.3^10 ] Genus 25 action of group of order 288 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-3 * G.1 * G.3^7 * G.2^-1 * G.3^-5 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-5 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 256 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3 ] Genus 25 action of group of order 224 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-22 * G.1 * G.2 * G.3^-5 ] Genus 25 action of group of order 208 via triangle group [ 2, 4, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-45 * G.1 * G.2 * G.3^-6 ] Genus 25 action of group of order 200 via triangle group [ 2, 4, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-43 * G.1 * G.2^-1 * G.3^-6 ] Genus 25 action of group of order 288 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3 * G.2^-1 * G.3)^3 ] Genus 25 action of group of order 288 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 288 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2^-2 * G.3)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 25 action of group of order 288 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 25 action of group of order 216 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 25 action of group of order 216 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 25 action of group of order 216 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 192 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 25 action of group of order 192 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2 ] Genus 25 action of group of order 168 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 162 via triangle group [ 2, 6, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^27 ] Genus 25 action of group of order 162 via triangle group [ 2, 6, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 162 via triangle group [ 2, 6, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 25 action of group of order 150 via triangle group [ 2, 6, 75 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^10 * G.2^-1 * G.3^-14 * G.1 ] Genus 25 action of group of order 160 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2^2 * G.3^-3 ] Genus 25 action of group of order 160 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.2^10 ] Genus 25 action of group of order 144 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3, G.2^12 ] Genus 25 action of group of order 144 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-12 ] Genus 25 action of group of order 144 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^5 * G.3^-3, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 25 action of group of order 120 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.2^12 ] Genus 25 action of group of order 120 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-15 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2^-5 * G.3^3)^2 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3^5 * G.2^-7 * G.3 * G.2^-2 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-11 * G.3 * G.2^-1 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.2^4 * G.3^-3 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^2 * G.3^-1 * G.2^2 * G.3^-3, G.1 * G.2^-4 * G.3^-1 * G.2^3 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-3 * G.3^-1 * G.1 * G.3 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-2 * G.3^3 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 25 action of group of order 128 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 25 action of group of order 110 via triangle group [ 2, 22, 55 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2^-6 * G.3^4 ] Genus 25 action of group of order 112 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-5 * G.2^11 * G.3^-1 * G.2^10 ] Genus 25 action of group of order 102 via triangle group [ 2, 51, 102 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^37 * G.2^-12 * G.3 ] Genus 25 action of group of order 104 via triangle group [ 2, 52, 52 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^38 * G.2^-13 ] Genus 25 action of group of order 100 via triangle group [ 2, 100, 100 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^49 * G.3^-1 ] Genus 25 action of group of order 360 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3^2 * G.2 * G.3^-1)^2 ] Genus 25 action of group of order 288 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, (G.1^-1 * G.2^-1 * G.3^-1)^4 ] Genus 25 action of group of order 288 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 25 action of group of order 192 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 25 action of group of order 180 via triangle group [ 3, 3, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1^-1 * G.3 * G.2)^2 ] Genus 25 action of group of order 180 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-2 * G.1 * G.3^2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 25 action of group of order 180 via triangle group [ 3, 3, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.3^-1 * G.2)^3 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 25 action of group of order 192 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 25 action of group of order 144 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 25 action of group of order 144 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 25 action of group of order 144 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 25 action of group of order 144 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 25 action of group of order 144 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.1 * G.3 * G.2)^2 ] Genus 25 action of group of order 144 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 25 action of group of order 144 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 25 action of group of order 120 via triangle group [ 3, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.1^-1 * G.3 * G.2)^2 ] Genus 25 action of group of order 108 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3 * G.2^-3 * G.3^2 * G.2^-2 ] Genus 25 action of group of order 108 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 25 action of group of order 108 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 160 via triangle group [ 4, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 25 action of group of order 160 via triangle group [ 4, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 25 action of group of order 160 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2 ] Genus 25 action of group of order 144 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6 ] Genus 25 action of group of order 144 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6 ] Genus 25 action of group of order 144 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^6 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^8 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.2 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.2 * G.3^-3)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^4 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^8 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.2^-1 * G.1 * G.3^2, G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.3^4 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-3)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-3)^2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.1^-1 * G.2 * G.1^-2 * G.3^3 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 ] Genus 25 action of group of order 128 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^2 * G.3 * G.2 ] Genus 25 action of group of order 112 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^5 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-6 * G.1^-1 ] Genus 25 action of group of order 104 via triangle group [ 4, 4, 26 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 * G.1 * G.2 * G.3^-10 ] Genus 25 action of group of order 104 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 25 action of group of order 104 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 25 action of group of order 100 via triangle group [ 4, 4, 50 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-19 * G.1^-1 * G.2 * G.3^-5 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 288 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^12 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^12 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^12 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 192 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^4 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-5 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5, (G.1 * G.2)^4 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.2 * G.1)^5 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-5 ] Genus 25 action of group of order 160 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^8 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^12 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, (G.3 * G.1)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.3 * G.1)^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.2)^4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.2)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, (G.2 * G.4^-1)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 128 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.1^2 * G.4^5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.2 * G.1)^5 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.3 * G.1)^5 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, (G.3 * G.1)^5 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.2 * G.1)^5 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.1^2 * G.4^5, (G.1 * G.2)^6 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.4^-4 * G.1 * G.2 * G.4^4, (G.3 * G.1)^6 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-6 * G.1^2 * G.4^-4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, (G.1 * G.2)^6 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-4 * G.1 * G.3 * G.1 * G.4^4 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6 * G.1^2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^10 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 ] Genus 25 action of group of order 120 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, (G.3 * G.1)^6 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-14 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-5 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-14 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^9 * G.1^2 * G.4^5 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^14 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^9 * G.1^2 * G.4^5 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.1 * G.4^5 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^14 ] Genus 25 action of group of order 112 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1^2 * G.4^-8 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^3 * G.1 * G.4 * G.1 * G.4^4 * G.3 * G.2 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.3 * G.1^2 * G.4^-4 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-5 * G.2 * G.1^2 * G.4^-4 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^2 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.1 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.4^-3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.4^-3 ] Genus 25 action of group of order 108 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, (G.3 * G.1)^6 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-5 * G.2 * G.4^6 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-6 * G.2 * G.1^2 * G.4^5 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8 * G.3 * G.1 * G.4^4 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-7 * G.1 * G.4^5 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1^2 * G.4^-7 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-26 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-21 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 25 action of group of order 104 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-15 * G.1 * G.2 * G.1 * G.2 * G.4^-9 ] Genus 25 action of group of order 100 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-12 * G.2 * G.3 * G.4^-12 ] Genus 25 action of group of order 100 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-20 * G.1 * G.3 * G.4^-4 ] Genus 25 action of group of order 100 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^14 * G.2 * G.1 * G.4^10 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.4 * G.3)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 25 action of group of order 144 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 25 has order 720 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 25 has order 1440 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 25 has order 1440 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 25 has order 288 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 26 has order 720 ... group action with signature (0; +; [-]; {(2,3,10)}) Check total 890 : 336 chiral, 554 reflexible, with 137 non-orientable quotient actions Genus 26 actions: Genus 26 action of group of order 750 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 26 action of group of order 660 via triangle group [ 2, 3, 11 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.2 * G.3^-5, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^3 ] Genus 26 action of group of order 216 via triangle group [ 2, 4, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-47 * G.1 * G.2 * G.3^-6 ] Genus 26 action of group of order 208 via triangle group [ 2, 4, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-45 * G.1 * G.2^-1 * G.3^-6 ] Genus 26 action of group of order 250 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 26 action of group of order 300 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 26 action of group of order 300 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 26 action of group of order 168 via triangle group [ 2, 6, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^14 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-5 * G.1 * G.3^2 ] Genus 26 action of group of order 156 via triangle group [ 2, 6, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^11 * G.2^-1 * G.1 * G.2^-1 * G.3^-13 * G.1 ] Genus 26 action of group of order 200 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2^-4 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 26 action of group of order 200 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 ] Genus 26 action of group of order 144 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^3 * G.2 * G.1 * G.3^8 * G.2^-1 * G.3^-5 * G.1 ] Genus 26 action of group of order 150 via triangle group [ 2, 10, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^6 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 26 action of group of order 130 via triangle group [ 2, 10, 65 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 26 action of group of order 120 via triangle group [ 2, 20, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.2^4 * G.3^-4 ] Genus 26 action of group of order 112 via triangle group [ 2, 28, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-3 * G.3^3 * G.2^-6 * G.3 * G.2^-1 ] Genus 26 action of group of order 106 via triangle group [ 2, 53, 106 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^39 * G.2^-12 * G.3 ] Genus 26 action of group of order 108 via triangle group [ 2, 54, 54 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^40 * G.2^-13 ] Genus 26 action of group of order 104 via triangle group [ 2, 104, 104 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^38 * G.2^-12 * G.3 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1, G.3^2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 600 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 375 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 26 action of group of order 168 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 26 action of group of order 168 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^2 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 26 action of group of order 300 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 26 action of group of order 150 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 26 action of group of order 150 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 26 action of group of order 200 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 26 action of group of order 108 via triangle group [ 4, 4, 27 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^17 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.1 * G.3^5 ] Genus 26 action of group of order 104 via triangle group [ 4, 4, 52 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-15 * G.1 * G.2^-1 * G.3^-10 ] Genus 26 action of group of order 125 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 26 action of group of order 300 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 26 action of group of order 200 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 26 action of group of order 108 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-13 * G.2 * G.1 * G.4^4 * G.3 * G.4^-9 ] Genus 26 action of group of order 108 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^22 * G.1^2 * G.4^5 ] Genus 26 action of group of order 108 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-17 * G.1 * G.2 * G.1 * G.2 * G.4^-8 ] Genus 26 action of group of order 104 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-13 * G.1 * G.4^-13 ] Genus 26 action of group of order 104 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-21 * G.2 * G.4^-5 ] Genus 26 action of group of order 104 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-16 * G.1 * G.2 * G.4^-9 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3^-1 * G.1 * G.3 * G.1)^5, G.2 * G.1^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, (G.2 * G.1)^5 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^10, G.2 * G.1^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, (G.2 * G.1)^5 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.4 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.4^-1 * G.2)^3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3^-1 * G.1)^3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.3 * G.1)^5 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.4^-1 * G.2^-1)^5, G.3 * G.1^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^2 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^5, G.3 * G.1^-1 ] Genus 26 action of group of order 150 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^2 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2^-1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.4^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 26 action of group of order 120 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.3 * G.2^-1)^3 ] Largest orientation-preserving group for genus 26 has order 750 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 26 has order 1500 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 26 has order 1500 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 26 has order 600 ... group action with signature (0: +; [3,3,4]; {-}) Largest non-orientable group for non-orientable genus 27 has order 300 ... group action with signature (0; +; [-]; {(2,2,2,3)}) Check total 203 : 118 chiral, 85 reflexible, with 19 non-orientable quotient actions Genus 27 actions: Genus 27 action of group of order 624 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 27 action of group of order 624 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 27 action of group of order 416 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 27 action of group of order 416 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 27 action of group of order 416 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 27 action of group of order 416 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 27 action of group of order 312 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 27 action of group of order 312 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 27 action of group of order 240 via triangle group [ 2, 4, 30 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-16 * G.1 * G.3^7 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 27 action of group of order 224 via triangle group [ 2, 4, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-22 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 27 action of group of order 224 via triangle group [ 2, 4, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-49 * G.1 * G.2 * G.3^-6 ] Genus 27 action of group of order 216 via triangle group [ 2, 4, 108 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-47 * G.1 * G.2^-1 * G.3^-6 ] Genus 27 action of group of order 240 via triangle group [ 2, 5, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 27 action of group of order 208 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 27 action of group of order 208 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 27 action of group of order 160 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^7 * G.2 * G.3^-5 * G.1 * G.3^7 ] Genus 27 action of group of order 160 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^20 ] Genus 27 action of group of order 144 via triangle group [ 2, 8, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^12 * G.2 * G.1 * G.3^5 ] Genus 27 action of group of order 144 via triangle group [ 2, 8, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.1 * G.3^11 * G.2 * G.3^-6 ] Genus 27 action of group of order 144 via triangle group [ 2, 9, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-9 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 27 action of group of order 156 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^2 ] Genus 27 action of group of order 126 via triangle group [ 2, 14, 63 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-4 * G.1 * G.2^-1 * G.3^-4 ] Genus 27 action of group of order 120 via triangle group [ 2, 20, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-8 * G.3^3 * G.2^-6 * G.3^3 ] Genus 27 action of group of order 120 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-26 * G.3 * G.2^-1 ] Genus 27 action of group of order 114 via triangle group [ 2, 38, 57 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-7 * G.3^3 * G.2^-9 ] Genus 27 action of group of order 110 via triangle group [ 2, 55, 110 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^41 * G.2^-12 * G.3 ] Genus 27 action of group of order 112 via triangle group [ 2, 56, 56 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^42 * G.2^-13 ] Genus 27 action of group of order 112 via triangle group [ 2, 56, 56 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-5 * G.2^11 * G.3^-1 * G.2^8 * G.3^-2 ] Genus 27 action of group of order 108 via triangle group [ 2, 108, 108 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^40 * G.2^-12 * G.3 ] Genus 27 action of group of order 312 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 27 action of group of order 312 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2 * G.3^-2 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^2 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 27 action of group of order 156 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 27 action of group of order 208 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 27 action of group of order 156 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 27 action of group of order 156 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 27 action of group of order 120 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 27 action of group of order 112 via triangle group [ 4, 4, 28 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2 * G.3^-6 * G.1 ] Genus 27 action of group of order 112 via triangle group [ 4, 4, 28 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^28 ] Genus 27 action of group of order 112 via triangle group [ 4, 4, 28 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2 * G.3^-6 * G.1^-1 ] Genus 27 action of group of order 112 via triangle group [ 4, 4, 28 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^5 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-6 * G.1 ] Genus 27 action of group of order 108 via triangle group [ 4, 4, 54 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^17 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.1^-1 * G.3^5 ] Genus 27 action of group of order 120 via triangle group [ 5, 5, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1 * G.3, G.1^-5, G.3^6 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 27 action of group of order 208 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, (G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 27 action of group of order 156 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^15 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-5 * G.2 * G.3 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.4^-4 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7 * G.2 * G.3 * G.2 * G.4^3 * G.3 * G.1 * G.4^-3 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-5 * G.2 * G.1 * G.4^4 * G.2 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^15 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-4 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^15 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^5 * G.2 * G.3 * G.4^-5 * G.1 * G.4^4 ] Genus 27 action of group of order 120 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-28 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-28 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-18 * G.1 * G.2 * G.1 * G.2 * G.4^-8 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-7 * G.2 * G.1 * G.4^5 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-8 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-7 * G.1 * G.4^-1 * G.1 * G.4^-6 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^8 * G.1 * G.3 * G.4^-5 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^9 * G.1^2 * G.2 * G.4 * G.2 * G.4^4 ] Genus 27 action of group of order 112 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^9 * G.1^2 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 27 action of group of order 108 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-13 * G.2 * G.3 * G.4^-13 ] Genus 27 action of group of order 108 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^21 * G.3 * G.1 * G.4^5 ] Genus 27 action of group of order 108 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-18 * G.1 * G.2 * G.4^-8 ] Largest orientation-preserving group for genus 27 has order 624 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 27 has order 624 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 27 has order 480 ... group action with signature (0; +; [-]; {(2,4,30)}) ... group action with signature (0; +; [-]; {(2,5,12)}) Largest chiral group for genus 27 has order 624 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 28 has order 240 ... group action with signature (0; +; [-]; {(2,4,30)}) Check total 187 : 122 chiral, 65 reflexible, with 26 non-orientable quotient actions Genus 28 actions: Genus 28 action of group of order 1296 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 1296 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 648 via triangle group [ 2, 3, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.3^12 ] Genus 28 action of group of order 648 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 28 action of group of order 486 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^5 * G.2 * G.3^-5 * G.1 * G.3, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 28 action of group of order 486 via triangle group [ 2, 3, 18 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 ] Genus 28 action of group of order 486 via triangle group [ 2, 3, 18 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 486 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^8 * G.2^-1 * G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 432 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.2 * G.3^-3 * G.1 * G.3, G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^5 ] Genus 28 action of group of order 648 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^6, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 28 action of group of order 432 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 432 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 28 action of group of order 232 via triangle group [ 2, 4, 58 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-51 * G.1 * G.2 * G.3^-6 ] Genus 28 action of group of order 224 via triangle group [ 2, 4, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-49 * G.1 * G.2^-1 * G.3^-6 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 28 action of group of order 324 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.1 * G.3^4 * G.2 * G.3^-7 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-3)^2 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 28 action of group of order 180 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^3 * G.2 * G.3^-1 * G.1 * G.3^5 ] Genus 28 action of group of order 180 via triangle group [ 2, 6, 30 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-10 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 28 action of group of order 180 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-6 * G.1 * G.3 * G.2 * G.1 * G.3^13 * G.2 * G.1 * G.2^-1 * G.3^-7 ] Genus 28 action of group of order 168 via triangle group [ 2, 6, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^20 * G.2 * G.1 * G.2 * G.3^-6 * G.1 ] Genus 28 action of group of order 216 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.3^-1 * G.1 * G.2^-3 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3 * G.2^-4 * G.3^-2 * G.1 * G.3 ] Genus 28 action of group of order 162 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.2^-9, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2 ] Genus 28 action of group of order 162 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^-9, G.1 * G.2^-4 * G.3^-3 * G.2 ] Genus 28 action of group of order 162 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-9 ] Genus 28 action of group of order 162 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 162 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 160 via triangle group [ 2, 10, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-6 ] Genus 28 action of group of order 140 via triangle group [ 2, 10, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.1 * G.3^7 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 144 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^-5 * G.3^-1 * G.1 * G.3^2 ] Genus 28 action of group of order 144 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^5 * G.3^-3, G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 28 action of group of order 144 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 28 action of group of order 126 via triangle group [ 2, 18, 63 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^4 ] Genus 28 action of group of order 126 via triangle group [ 2, 21, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-1 * G.3^3 * G.2^-1 * G.3^5 * G.2^-8 * G.3^2 * G.2^-1 ] Genus 28 action of group of order 120 via triangle group [ 2, 30, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-7 * G.2^11 * G.3^-1 * G.2^8 * G.3^-2 ] Genus 28 action of group of order 114 via triangle group [ 2, 57, 114 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^43 * G.2^-12 * G.3 ] Genus 28 action of group of order 116 via triangle group [ 2, 58, 58 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^44 * G.2^-13 ] Genus 28 action of group of order 112 via triangle group [ 2, 112, 112 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^42 * G.2^-12 * G.3 ] Genus 28 action of group of order 648 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 648 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 324 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 28 action of group of order 324 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-9 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 28 action of group of order 243 via triangle group [ 3, 3, 9 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 28 action of group of order 189 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1^-1 * G.2^-1 * G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 189 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 28 action of group of order 171 via triangle group [ 3, 3, 57 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 28 action of group of order 171 via triangle group [ 3, 3, 57 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 28 action of group of order 324 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3 ] Genus 28 action of group of order 216 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 28 action of group of order 216 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 28 action of group of order 216 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 28 action of group of order 216 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 28 action of group of order 216 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 144 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 28 action of group of order 180 via triangle group [ 3, 5, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-5, (G.3^-1 * G.2)^3 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2^6 ] Genus 28 action of group of order 162 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1 * G.2^3 * G.3^-2 * G.2 ] Genus 28 action of group of order 144 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 28 action of group of order 126 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1 * G.2^-2 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 126 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 ] Genus 28 action of group of order 114 via triangle group [ 3, 6, 38 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 28 action of group of order 114 via triangle group [ 3, 6, 38 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-2 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 28 action of group of order 216 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 28 action of group of order 216 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 ] Genus 28 action of group of order 116 via triangle group [ 4, 4, 29 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^29 ] Genus 28 action of group of order 116 via triangle group [ 4, 4, 29 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 28 action of group of order 116 via triangle group [ 4, 4, 29 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.3^-3 ] Genus 28 action of group of order 112 via triangle group [ 4, 4, 56 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^17 * G.2 * G.1^-1 * G.3^10 ] Genus 28 action of group of order 120 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-1)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-1)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6 ] Genus 28 action of group of order 324 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 216 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, (G.2 * G.4^-2)^2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 144 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2 ] Genus 28 action of group of order 116 via quadrangle group [ 2, 2, 2, 29 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-14 * G.2 * G.1 * G.4^4 * G.3 * G.4^-10 ] Genus 28 action of group of order 116 via quadrangle group [ 2, 2, 2, 29 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-23 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 28 action of group of order 116 via quadrangle group [ 2, 2, 2, 29 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-18 * G.1 * G.2 * G.1 * G.2 * G.4^-9 ] Genus 28 action of group of order 112 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-14 * G.1 * G.4^-14 ] Genus 28 action of group of order 112 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-22 * G.1 * G.3 * G.4^-5 ] Genus 28 action of group of order 112 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-19 * G.1 * G.2 * G.4^-8 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.1 * G.3^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-2 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 28 action of group of order 162 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Largest orientation-preserving group for genus 28 has order 1296 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 28 has order 1296 ... group action with signature (0: +; [2,3,8]; {-}) ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 28 has order 1296 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 28 has order 1296 ... group action with signature (0: +; [2,3,8]; {-}) Largest non-orientable group for non-orientable genus 29 has order 648 ... group action with signature (0; +; [-]; {(2,3,12)}) Check total 410 : 224 chiral, 186 reflexible, with 28 non-orientable quotient actions Genus 29 actions: Genus 29 action of group of order 672 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 29 action of group of order 288 via triangle group [ 2, 4, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 256 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-18 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-5 ] Genus 29 action of group of order 256 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 29 action of group of order 240 via triangle group [ 2, 4, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-60 ] Genus 29 action of group of order 232 via triangle group [ 2, 4, 116 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-51 * G.1 * G.2^-1 * G.3^-6 ] Genus 29 action of group of order 320 via triangle group [ 2, 5, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 29 action of group of order 320 via triangle group [ 2, 5, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2 ] Genus 29 action of group of order 336 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 29 action of group of order 336 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 336 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 29 action of group of order 336 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 29 action of group of order 336 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 29 action of group of order 240 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 29 action of group of order 240 via triangle group [ 2, 6, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.3^-3 ] Genus 29 action of group of order 240 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3 * G.2)^2 ] Genus 29 action of group of order 210 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 29 action of group of order 210 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 192 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4 ] Genus 29 action of group of order 192 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 174 via triangle group [ 2, 6, 87 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3^13 * G.2 * G.1 * G.3^7 * G.2^-1 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^12 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^-1 * G.1 * G.2^-3 * G.3^-4 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^-3 * G.3^-2 * G.1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^6 * G.2 * G.3^-5 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-12 ] Genus 29 action of group of order 192 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-12 ] Genus 29 action of group of order 160 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^7 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 29 action of group of order 160 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.1 * G.3^13 * G.2^-1 * G.3^-6 ] Genus 29 action of group of order 168 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-2 * G.3^2 * G.2^-5 * G.3 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3^2 * G.2^-5 * G.3 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.2^-12 ] Genus 29 action of group of order 168 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^-12 ] Genus 29 action of group of order 144 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-2 * G.2^10 * G.3^-2 * G.2^2 ] Genus 29 action of group of order 128 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-8 * G.2^11 * G.3^-1 * G.2^9 * G.3^-1 * G.2 ] Genus 29 action of group of order 128 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3^2 * G.2^-11 * G.3^2 ] Genus 29 action of group of order 128 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3^5 * G.2^-9 * G.3 ] Genus 29 action of group of order 128 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-5 * G.3^3 * G.2^-6 * G.3 * G.2^-1 ] Genus 29 action of group of order 118 via triangle group [ 2, 59, 118 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^45 * G.2^-12 * G.3 ] Genus 29 action of group of order 120 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^46 * G.2^-13 ] Genus 29 action of group of order 116 via triangle group [ 2, 116, 116 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^44 * G.2^-12 * G.3 ] Genus 29 action of group of order 336 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 29 action of group of order 192 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3 * G.2, G.2^-2 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.2^-2 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2^-2 * G.1 * G.3 * G.2^-2 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2^-2 * G.1 * G.3 * G.2^-2 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^3 * G.3^-2 * G.2 ] Genus 29 action of group of order 168 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.1 * G.2^3 * G.3^-2 * G.2 ] Genus 29 action of group of order 120 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^3 * G.1^-1 * G.2^-1 * G.3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 29 action of group of order 120 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 120 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1 * G.2^2)^2 ] Genus 29 action of group of order 144 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^4 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 144 via triangle group [ 4, 4, 9 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-3 ] Genus 29 action of group of order 144 via triangle group [ 4, 4, 9 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^3 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2 * G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-11 * G.1^-1 * G.3^2 * G.2 * G.3^-2 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-6 * G.1^-1 * G.2^-1 * G.3^-5 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 29 action of group of order 128 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 29 action of group of order 120 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 120 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 29 action of group of order 120 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^30 ] Genus 29 action of group of order 116 via triangle group [ 4, 4, 58 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^18 * G.2 * G.1^-1 * G.3^10 ] Genus 29 action of group of order 160 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 29 action of group of order 160 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 29 action of group of order 120 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^6 ] Genus 29 action of group of order 120 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 29 action of group of order 336 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^14 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^14 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 224 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-9 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-9 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^5 * G.1^2 * G.4^4 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^5 * G.1^2 * G.4^4 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^5 * G.1^2 * G.4^4 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^5 * G.1^2 * G.4^4 ] Genus 29 action of group of order 144 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.1^2 * G.4^4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 140 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-16 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^7 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^6 * G.3 * G.1 * G.4 * G.2 * G.4^8 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.1 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.1 * G.4^5 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^16 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-8 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 128 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-8 * G.2 * G.4^5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.1^2 * G.4^5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-9 * G.1 * G.4^5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10 * G.3 * G.1 * G.4^4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^9 * G.1^2 * G.2 * G.4^-4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1^2 * G.4^-9 * G.1 * G.4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.4 * G.3 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-5 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-30 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-24 * G.1^2 * G.4^-6 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-22 * G.1 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 29 action of group of order 116 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-14 * G.2 * G.3 * G.4^-14 ] Genus 29 action of group of order 116 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-23 * G.2 * G.4^-6 ] Genus 29 action of group of order 116 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-18 * G.1 * G.2 * G.1^2 * G.4^-10 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^7, (G.3 * G.1 * G.3^-1 * G.1)^4, G.2 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3^-1 * G.1)^3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.4^-1 * G.2)^3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.3^-1 * G.1)^3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, (G.3 * G.4^-1)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.3^-1 * G.1)^3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.1 * G.4 * G.3^-1 * G.1 * G.4^-2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3^-1 * G.2 * G.4^-2, (G.3 * G.4^-2)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.2 * G.1)^3, (G.3 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.1 * G.4^-2, (G.3 * G.4^-2)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.4^-1)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.3 * G.4^-1)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.3)^3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.3 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.2 * G.4^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, (G.1 * G.4 * G.2)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2^-1 * G.1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, (G.2^-1 * G.4^-1)^4, G.3 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 29 action of group of order 168 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, (G.2 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.4 * G.3 * G.1 * G.4^2, (G.4^-1 * G.2^-1)^3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.1 * G.4, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.3 * G.1)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2, (G.4^-1 * G.2^-1)^3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.4^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.4^-2)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, (G.1 * G.4 * G.3)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.2^-1 * G.3 * G.1)^2 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2^-1 * G.4, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-5 ] Genus 29 action of group of order 120 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Largest orientation-preserving group for genus 29 has order 672 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 29 has order 1344 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 29 has order 1344 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 29 has order 336 ... group action with signature (0: +; [2,6,6]; {-}) ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 30 has order 672 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 651 : 382 chiral, 269 reflexible, with 110 non-orientable quotient actions Genus 30 actions: Genus 30 action of group of order 264 via triangle group [ 2, 4, 33 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-19 * G.1 * G.3^7 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 30 action of group of order 248 via triangle group [ 2, 4, 62 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-62 ] Genus 30 action of group of order 240 via triangle group [ 2, 4, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-53 * G.1 * G.2^-1 * G.3^-6 ] Genus 30 action of group of order 192 via triangle group [ 2, 6, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-8 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 30 action of group of order 176 via triangle group [ 2, 8, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-3 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 30 action of group of order 168 via triangle group [ 2, 12, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-2 * G.1 * G.3^5 * G.2^-1 * G.3^-6 ] Genus 30 action of group of order 140 via triangle group [ 2, 14, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-4, (G.2^-2 * G.3^4 * G.2^-1)^2 ] Genus 30 action of group of order 132 via triangle group [ 2, 22, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-9 * G.3^2 * G.2^-7 * G.3^2 * G.2^-2 ] Genus 30 action of group of order 130 via triangle group [ 2, 26, 65 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2 * G.3^-4 * G.1, G.2 * G.3^-4 * G.2^6 * G.3^-1 * G.2 ] Genus 30 action of group of order 132 via triangle group [ 2, 33, 33 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-29 * G.3 * G.2^-1 ] Genus 30 action of group of order 122 via triangle group [ 2, 61, 122 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^47 * G.2^-12 * G.3 ] Genus 30 action of group of order 124 via triangle group [ 2, 62, 62 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^48 * G.2^-13 ] Genus 30 action of group of order 120 via triangle group [ 2, 120, 120 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^46 * G.2^-12 * G.3 ] Genus 30 action of group of order 183 via triangle group [ 3, 3, 61 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.3^-4 * G.1^-1 * G.3^4 ] Genus 30 action of group of order 183 via triangle group [ 3, 3, 61 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.3^4 ] Genus 30 action of group of order 124 via triangle group [ 4, 4, 31 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^31 ] Genus 30 action of group of order 120 via triangle group [ 4, 4, 60 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^19 * G.2 * G.1^-1 * G.3^10 ] Genus 30 action of group of order 120 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^5 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 30 action of group of order 120 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^2 * G.2^-1 * G.1 * G.3^2 ] Genus 30 action of group of order 124 via quadrangle group [ 2, 2, 2, 31 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-15 * G.2 * G.1 * G.4^4 * G.3 * G.4^-11 ] Genus 30 action of group of order 124 via quadrangle group [ 2, 2, 2, 31 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-25 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 30 action of group of order 124 via quadrangle group [ 2, 2, 2, 31 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-31 ] Genus 30 action of group of order 120 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-15 * G.1 * G.4^-15 ] Genus 30 action of group of order 120 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-24 * G.1 * G.3 * G.4^-5 ] Genus 30 action of group of order 120 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-23 * G.1 * G.2 * G.4^-6 ] Largest orientation-preserving group for genus 30 has order 264 ... group action with signature (0: +; [2,4,33]; {-}) Largest group with or without reflections for genus 30 has order 528 ... group action with signature (0; +; [-]; {(2,4,33)}) Largest group with reflections for genus 30 has order 528 ... group action with signature (0; +; [-]; {(2,4,33)}) No chiral group action for genus 30 Largest non-orientable group for non-orientable genus 31 has order 264 ... group action with signature (0; +; [-]; {(2,4,33)}) Check total 25 : 0 chiral, 25 reflexible, with 6 non-orientable quotient actions Genus 31 actions: Genus 31 action of group of order 504 via triangle group [ 2, 3, 21 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 31 action of group of order 450 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2^-1 * G.3^-3 ] Genus 31 action of group of order 720 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 31 action of group of order 336 via triangle group [ 2, 4, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 31 action of group of order 336 via triangle group [ 2, 4, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 31 action of group of order 320 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 31 action of group of order 320 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 31 action of group of order 320 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 31 action of group of order 320 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^7 * G.2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 31 action of group of order 288 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3 ] Genus 31 action of group of order 288 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, (G.2^-1 * G.3)^6 ] Genus 31 action of group of order 280 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 31 action of group of order 280 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-6 ] Genus 31 action of group of order 256 via triangle group [ 2, 4, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-17 * G.1 * G.3^6 * G.2 * G.3^-8 ] Genus 31 action of group of order 256 via triangle group [ 2, 4, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-64 ] Genus 31 action of group of order 248 via triangle group [ 2, 4, 124 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-55 * G.1 * G.2^-1 * G.3^-6 ] Genus 31 action of group of order 240 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.3 * G.2^-1 * G.3)^3 ] Genus 31 action of group of order 360 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 ] Genus 31 action of group of order 198 via triangle group [ 2, 6, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^19 * G.2 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^4 ] Genus 31 action of group of order 186 via triangle group [ 2, 6, 93 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^15 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-6 * G.1 * G.3 ] Genus 31 action of group of order 150 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2^-1 * G.3^3 * G.2^-3 * G.3 * G.2^-7 ] Genus 31 action of group of order 160 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^5 * G.2^-7 * G.3 * G.2^-2 ] Genus 31 action of group of order 160 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 ] Genus 31 action of group of order 160 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-4 * G.2^7 * G.3^-4 * G.2 ] Genus 31 action of group of order 160 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 31 action of group of order 144 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3 * G.2^-4 * G.3^2 * G.2^-1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-11 * G.3^2 * G.2^-7 * G.3^2 * G.2^-2 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-1 * G.3^7 * G.2^-1 * G.3^5 * G.2^-7 * G.3 * G.2^-1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3 * G.2^-4 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^4 * G.3^-3 * G.2 ] Genus 31 action of group of order 140 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-3 * G.3 * G.2^-5 * G.3^2 * G.2^-1 * G.3 ] Genus 31 action of group of order 140 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-4 * G.3 * G.2^-6 * G.3 * G.2^-1 * G.3 ] Genus 31 action of group of order 126 via triangle group [ 2, 63, 126 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^49 * G.2^-12 * G.3 ] Genus 31 action of group of order 128 via triangle group [ 2, 64, 64 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^50 * G.2^-13 ] Genus 31 action of group of order 128 via triangle group [ 2, 64, 64 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-8 * G.2^11 * G.3^-1 * G.2^10 * G.3^-1 ] Genus 31 action of group of order 124 via triangle group [ 2, 124, 124 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^48 * G.2^-12 * G.3 ] Genus 31 action of group of order 225 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 31 action of group of order 360 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 31 action of group of order 168 via triangle group [ 3, 6, 7 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 150 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 144 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 31 action of group of order 144 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 31 action of group of order 126 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 126 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-2 ] Genus 31 action of group of order 168 via triangle group [ 4, 4, 7 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2, G.3^2 * G.2 * G.1 * G.3^-1 * G.1^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^8 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^8 ] Genus 31 action of group of order 160 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 31 action of group of order 144 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^2 * G.2 * G.1^-1 * G.3^3 ] Genus 31 action of group of order 144 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 31 action of group of order 144 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2 ] Genus 31 action of group of order 140 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3^4 ] Genus 31 action of group of order 140 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^4 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2 * G.3^-3 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-11 * G.1 * G.3^2 * G.2 * G.3^-2 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^10 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-6 * G.1^-1 * G.2^-1 * G.3^-5 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-21 * G.1 * G.2 * G.3^-10 ] Genus 31 action of group of order 128 via triangle group [ 4, 4, 32 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^10 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 31 action of group of order 124 via triangle group [ 4, 4, 62 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^21 * G.2 * G.1^-1 * G.3^9 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^6, G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-2)^2, G.2^6, G.3^6 ] Genus 31 action of group of order 144 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, (G.1 * G.3^-2)^2, G.3^6 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.2 * G.1 * G.3)^3, (G.1 * G.3)^6 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 31 action of group of order 360 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.2 * G.4^-1)^4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.1 * G.3)^10 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.3 * G.1)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^15 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 31 action of group of order 240 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^15 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-7 ] Genus 31 action of group of order 168 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-7 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.4^8, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 160 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 150 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 31 action of group of order 150 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 31 action of group of order 150 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 31 action of group of order 150 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-3 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-6 * G.1 * G.2 * G.3 * G.4^-5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.1 * G.4^5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^7 * G.1^2 * G.4^5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-3 * G.2 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^12 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4^5 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.3 * G.1)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, (G.1 * G.2)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^2 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 31 action of group of order 140 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^6 * G.1 * G.4^5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.1 * G.3 * G.1 * G.2 * G.4^5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^5 * G.1 * G.3 * G.1 * G.4^-5 * G.2 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^5 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^4 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.3 * G.1 * G.4^4 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-7 * G.2 * G.1^2 * G.4^-4 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 31 action of group of order 132 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-32 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^32 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^24 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-9 * G.2 * G.1 * G.4^5 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^9 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^7 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^6 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-8 * G.1 * G.4^-1 * G.1 * G.4^-7 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^6 * G.3 * G.1 * G.4^-8 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.3 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^6 * G.3 * G.1 * G.2 * G.4^9 ] Genus 31 action of group of order 128 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4^5 ] Genus 31 action of group of order 124 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-15 * G.2 * G.3 * G.4^-15 ] Genus 31 action of group of order 124 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-25 * G.2 * G.1^2 * G.4^-6 ] Genus 31 action of group of order 124 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-19 * G.1 * G.2 * G.4^-11 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1)^3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.2)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.3^-1 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.2^-1)^3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.2^-1)^3, (G.3 * G.1)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.4^-1 * G.2^-1)^5, G.3 * G.1^-1 ] Genus 31 action of group of order 180 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^5, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.3 * G.1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.3 * G.1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2 ] Genus 31 action of group of order 144 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Largest orientation-preserving group for genus 31 has order 720 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 31 has order 1440 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 31 has order 1440 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 31 has order 360 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 32 has order 720 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 674 : 396 chiral, 278 reflexible, with 115 non-orientable quotient actions Genus 32 actions: Genus 32 action of group of order 264 via triangle group [ 2, 4, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-66 ] Genus 32 action of group of order 256 via triangle group [ 2, 4, 128 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-57 * G.1 * G.2^-1 * G.3^-6 ] Genus 32 action of group of order 310 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 32 action of group of order 310 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 32 action of group of order 310 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 32 action of group of order 310 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 32 action of group of order 372 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 32 action of group of order 372 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 32 action of group of order 372 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 32 action of group of order 372 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 32 action of group of order 204 via triangle group [ 2, 6, 34 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-19 * G.1 * G.3^5 * G.2^-1 * G.3^-9 ] Genus 32 action of group of order 192 via triangle group [ 2, 6, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^18 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 32 action of group of order 176 via triangle group [ 2, 8, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-3 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-14 ] Genus 32 action of group of order 180 via triangle group [ 2, 10, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-2 * G.1 * G.3^9 * G.2^-1 * G.3^-6 ] Genus 32 action of group of order 160 via triangle group [ 2, 10, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^7 * G.2 * G.3^-2 * G.1 * G.3^6 ] Genus 32 action of group of order 160 via triangle group [ 2, 16, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-3 ] Genus 32 action of group of order 144 via triangle group [ 2, 18, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-5 * G.3^4 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 32 action of group of order 136 via triangle group [ 2, 34, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-10 * G.2^21 * G.3^-2 ] Genus 32 action of group of order 130 via triangle group [ 2, 65, 130 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^51 * G.2^-12 * G.3 ] Genus 32 action of group of order 132 via triangle group [ 2, 66, 66 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^52 * G.2^-13 ] Genus 32 action of group of order 128 via triangle group [ 2, 128, 128 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^50 * G.2^-12 * G.3 ] Genus 32 action of group of order 186 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 32 action of group of order 186 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 32 action of group of order 186 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^3 * G.3^-1 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 32 action of group of order 132 via triangle group [ 4, 4, 33 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-21 * G.1 * G.2 * G.3^-11 ] Genus 32 action of group of order 128 via triangle group [ 4, 4, 64 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-21 * G.1 * G.2^-1 * G.3^-10 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2, G.2^-5 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1 * G.2^-2 * G.1 * G.3 * G.2, G.2^-5 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.3^-2 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-2 * G.2 * G.1 * G.3 * G.2 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2^-5 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.2^-1 * G.3^-1 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1, G.2^-5 ] Genus 32 action of group of order 155 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1 * G.2^-1 * G.1^2 * G.3 * G.2 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^6 * G.1^2 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-5 * G.1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-4 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^6 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^5 * G.3 * G.1 * G.2 * G.4^5 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^5 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-16 * G.2 * G.1 * G.3 * G.4^-16 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-26 * G.1^2 * G.4^-7 ] Genus 32 action of group of order 132 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^13 * G.2 * G.4^-13 * G.1 * G.2 * G.1 * G.4^5 ] Genus 32 action of group of order 128 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-16 * G.1 * G.4^-16 ] Genus 32 action of group of order 128 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^26 * G.2 * G.4^6 ] Genus 32 action of group of order 128 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^24 * G.2 * G.1 * G.4^7 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.1^2 * G.3 * G.2 * G.4, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-2 * G.4^-1 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-2 * G.4^-1 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2^-1 * G.4^-1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 32 action of group of order 186 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Largest orientation-preserving group for genus 32 has order 372 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 32 has order 528 ... group action with signature (0; +; [-]; {(2,4,66)}) Largest group with reflections for genus 32 has order 528 ... group action with signature (0; +; [-]; {(2,4,66)}) Largest chiral group for genus 32 has order 372 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 33 has order 204 ... group action with signature (0; +; [-]; {(2,6,34)}) Check total 179 : 144 chiral, 35 reflexible, with 10 non-orientable quotient actions Genus 33 actions: Genus 33 action of group of order 1536 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 768 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 768 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12, G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 768 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 33 action of group of order 768 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 33 action of group of order 768 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.3^-2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 768 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 512 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 * G.1, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 * G.1 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2^-1 * G.3^2)^4 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^5 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-12 ] Genus 33 action of group of order 320 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-3 * G.1 * G.3^10 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 33 action of group of order 288 via triangle group [ 2, 4, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-20 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 33 action of group of order 288 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 33 action of group of order 288 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-22 * G.1 * G.3^7 * G.2^-1 * G.3^-6 ] Genus 33 action of group of order 272 via triangle group [ 2, 4, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-60 * G.1 * G.2 * G.3^-7 ] Genus 33 action of group of order 264 via triangle group [ 2, 4, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-59 * G.1 * G.2^-1 * G.3^-6 ] Genus 33 action of group of order 320 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.3, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6, (G.2 * G.3^-1 * G.2)^4 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 384 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2 ] Genus 33 action of group of order 336 via triangle group [ 2, 6, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2 * G.2)^2, G.3^-3 * G.1 * G.2 * G.3^-3 ] Genus 33 action of group of order 336 via triangle group [ 2, 6, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-3 * G.1 * G.2 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^8 ] Genus 33 action of group of order 256 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^2 * G.2^-3 * G.3^-2 * G.1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^6 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-5 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^6 * G.2 * G.3^-5 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-6 * G.1 * G.3^2 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-6 ] Genus 33 action of group of order 176 via triangle group [ 2, 8, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.1 * G.3^6 * G.2^-1 * G.3^-15 ] Genus 33 action of group of order 176 via triangle group [ 2, 8, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-15 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^12 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-12 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 33 action of group of order 192 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^5 * G.3^-1 * G.2 * G.3^-1 ] Genus 33 action of group of order 168 via triangle group [ 2, 12, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 33 action of group of order 154 via triangle group [ 2, 14, 77 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-5 ] Genus 33 action of group of order 160 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^6 * G.3^-1 * G.2^7 * G.3^-2 * G.2 ] Genus 33 action of group of order 144 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-32 * G.3 * G.2^-1 ] Genus 33 action of group of order 144 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-1 * G.2 * G.3^-2 * G.2^10 * G.3^-4 ] Genus 33 action of group of order 144 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-12 * G.2^24 ] Genus 33 action of group of order 138 via triangle group [ 2, 46, 69 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3 * G.2^-9 * G.3^2 * G.2^-7 * G.3^4 ] Genus 33 action of group of order 134 via triangle group [ 2, 67, 134 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^53 * G.2^-12 * G.3 ] Genus 33 action of group of order 136 via triangle group [ 2, 68, 68 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^54 * G.2^-13 ] Genus 33 action of group of order 132 via triangle group [ 2, 132, 132 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^52 * G.2^-12 * G.3 ] Genus 33 action of group of order 768 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.1 * G.3 * G.2)^4 ] Genus 33 action of group of order 384 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 33 action of group of order 384 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 384 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 33 action of group of order 384 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 33 action of group of order 384 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 33 action of group of order 201 via triangle group [ 3, 3, 67 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2 * G.3^-1 * G.1^-2 * G.3^4 ] Genus 33 action of group of order 201 via triangle group [ 3, 3, 67 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.3^-1 * G.2)^3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 33 action of group of order 384 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3 * G.2)^2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 192 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, (G.2 * G.3^-1)^4 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 33 action of group of order 168 via triangle group [ 3, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-7 ] Genus 33 action of group of order 168 via triangle group [ 3, 7, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-7, (G.2 * G.3^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 33 action of group of order 256 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-2 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.3^2 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^6 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, (G.2^-1 * G.1)^3, G.3^6 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.2^-1 * G.1)^3, G.3^6 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^6, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^6, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 33 action of group of order 192 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 33 action of group of order 160 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^10 ] Genus 33 action of group of order 160 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 160 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 33 action of group of order 144 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-13 * G.1 * G.2 * G.3^-4 ] Genus 33 action of group of order 144 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 33 action of group of order 144 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^18 ] Genus 33 action of group of order 144 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 33 action of group of order 144 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 33 action of group of order 136 via triangle group [ 4, 4, 34 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 33 action of group of order 136 via triangle group [ 4, 4, 34 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 33 action of group of order 136 via triangle group [ 4, 4, 34 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-22 * G.1 * G.2 * G.3^-11 ] Genus 33 action of group of order 132 via triangle group [ 4, 4, 66 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-21 * G.1 * G.2^-1 * G.3^-11 ] Genus 33 action of group of order 160 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, (G.1 * G.2^-2)^2, G.2^-5, G.3 * G.2 * G.1^-2 * G.2 * G.3^-1 * G.1 ] Genus 33 action of group of order 160 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2)^2, G.2^2 * G.1^-2 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 160 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 384 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^8 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^16 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^16 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 256 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^8 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^8 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.3 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.1^2 * G.4^4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^6 * G.1^2 * G.4^4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.1^2 * G.4^4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^6 * G.1^2 * G.4^4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 33 action of group of order 160 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^10 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-6 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^9 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-10 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-11 * G.1 * G.2 * G.4^6 * G.3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-12 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.4^5 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^7 * G.3 * G.2 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.3 * G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4^4 * G.1 * G.3 * G.2 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.4^-1 * G.2 * G.4^2 * G.1 * G.4^5 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-6 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^18 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^7 * G.2 * G.4^-7 * G.1 * G.4^3 ] Genus 33 action of group of order 144 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-5 * G.1 * G.4^8 * G.1 * G.4^-2 * G.1 * G.4^2 * G.2 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-9 * G.2 * G.4 * G.1^2 * G.4^5 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-9 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-12 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^4 * G.2 * G.4^-2 * G.1 * G.4^10 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4 * G.2 * G.1^2 * G.4^-6 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-34 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-27 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 33 action of group of order 136 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-27 * G.1^2 * G.4^-7 ] Genus 33 action of group of order 132 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-16 * G.2 * G.3 * G.4^-16 ] Genus 33 action of group of order 132 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-26 * G.1 * G.3 * G.4^-6 ] Genus 33 action of group of order 132 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^13 * G.2 * G.4^-13 * G.1 * G.4^6 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.4^-1 * G.2)^3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.3^-1 * G.1)^3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1)^4, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^8, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.3^-1)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.3^-1)^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.3 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1)^4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2)^3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.3)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.3)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.1 * G.3)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.1)^4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.3 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.3 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^4, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1)^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, (G.2^-1 * G.1)^4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1)^4, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 33 action of group of order 192 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Largest orientation-preserving group for genus 33 has order 1536 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 33 has order 3072 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 33 has order 3072 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 33 has order 768 ... group action with signature (0: +; [2,3,12]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest non-orientable group for non-orientable genus 34 has order 384 ... group action with signature (0; +; [-]; {(2,4,12)}) ... group action with signature (0; +; [-]; {(2,2,2,3)}) Check total 1050 : 418 chiral, 632 reflexible, with 129 non-orientable quotient actions Genus 34 actions: Genus 34 action of group of order 1320 via triangle group [ 2, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 34 action of group of order 1320 via triangle group [ 2, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 34 action of group of order 360 via triangle group [ 2, 4, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 34 action of group of order 280 via triangle group [ 2, 4, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-62 * G.1 * G.2 * G.3^-7 ] Genus 34 action of group of order 272 via triangle group [ 2, 4, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-60 * G.1 * G.2^-1 * G.3^-7 ] Genus 34 action of group of order 660 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 34 action of group of order 660 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 34 action of group of order 216 via triangle group [ 2, 6, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 34 action of group of order 216 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^14 * G.2 * G.3^-2 * G.1 * G.3^8 * G.2 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3 ] Genus 34 action of group of order 216 via triangle group [ 2, 6, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-5 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 34 action of group of order 216 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^21 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^7 ] Genus 34 action of group of order 204 via triangle group [ 2, 6, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-15 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.3^-6 * G.1 * G.3^2 * G.2^-1 ] Genus 34 action of group of order 240 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^3 * G.1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 34 action of group of order 216 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 34 action of group of order 216 via triangle group [ 2, 9, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^4 ] Genus 34 action of group of order 216 via triangle group [ 2, 9, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^2 * G.3^-4 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-4, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2^10 ] Genus 34 action of group of order 220 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^10 ] Genus 34 action of group of order 170 via triangle group [ 2, 10, 85 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.1 * G.3^6 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-6 ] Genus 34 action of group of order 168 via triangle group [ 2, 12, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-5 ] Genus 34 action of group of order 180 via triangle group [ 2, 15, 15 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 ] Genus 34 action of group of order 144 via triangle group [ 2, 36, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-3 * G.3^4 * G.2^-4 * G.3^3 * G.2^-1 * G.3 ] Genus 34 action of group of order 138 via triangle group [ 2, 69, 138 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^55 * G.2^-12 * G.3 ] Genus 34 action of group of order 140 via triangle group [ 2, 70, 70 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^56 * G.2^-13 ] Genus 34 action of group of order 136 via triangle group [ 2, 136, 136 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^54 * G.2^-12 * G.3 ] Genus 34 action of group of order 144 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 34 action of group of order 144 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 34 action of group of order 144 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 ] Genus 34 action of group of order 140 via triangle group [ 4, 4, 35 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^22 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 34 action of group of order 140 via triangle group [ 4, 4, 35 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 34 action of group of order 140 via triangle group [ 4, 4, 35 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 ] Genus 34 action of group of order 136 via triangle group [ 4, 4, 68 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-22 * G.1 * G.2^-1 * G.3^-11 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.2^-2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.3^-2 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 34 action of group of order 144 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 34 action of group of order 264 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.1 * G.4^-4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-17 * G.2 * G.1 * G.3 * G.4^-17 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-28 * G.1^2 * G.4^-7 ] Genus 34 action of group of order 140 via quadrangle group [ 2, 2, 2, 35 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-28 * G.1^2 * G.4^-7 ] Genus 34 action of group of order 136 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-17 * G.1 * G.4^-17 ] Genus 34 action of group of order 136 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-27 * G.2 * G.1^2 * G.4^-7 ] Genus 34 action of group of order 136 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-26 * G.1 * G.2 * G.1^2 * G.4^-7 ] Largest orientation-preserving group for genus 34 has order 1320 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 34 has order 2640 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 34 has order 2640 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 34 has order 264 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 35 has order 1320 ... group action with signature (0; +; [-]; {(2,4,5)}) Check total 105 : 58 chiral, 47 reflexible, with 12 non-orientable quotient actions Genus 35 actions: Genus 35 action of group of order 544 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 35 action of group of order 544 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 35 action of group of order 544 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 35 action of group of order 544 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 35 action of group of order 408 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 35 action of group of order 408 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 35 action of group of order 288 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-22 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 35 action of group of order 288 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-64 * G.1 * G.2 * G.3^-7 ] Genus 35 action of group of order 280 via triangle group [ 2, 4, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-62 * G.1 * G.2^-1 * G.3^-7 ] Genus 35 action of group of order 240 via triangle group [ 2, 6, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 35 action of group of order 240 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 35 action of group of order 210 via triangle group [ 2, 6, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^11 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-7 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 35 action of group of order 272 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 35 action of group of order 192 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^7 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-8 * G.1 ] Genus 35 action of group of order 192 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-5 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 35 action of group of order 204 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 35 action of group of order 204 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 35 action of group of order 192 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 35 action of group of order 192 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^7 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 35 action of group of order 168 via triangle group [ 2, 12, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1, G.2^12 ] Genus 35 action of group of order 160 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.1 * G.3^5 ] Genus 35 action of group of order 160 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3, (G.2^-5 * G.3^3)^2 ] Genus 35 action of group of order 160 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3^8 * G.2^-11 ] Genus 35 action of group of order 160 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-9 * G.3^3 * G.2^-5 * G.3^3 ] Genus 35 action of group of order 168 via triangle group [ 2, 21, 21 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^2 * G.3^-8 * G.2^8 * G.3^-3 ] Genus 35 action of group of order 168 via triangle group [ 2, 21, 21 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^2 * G.3^-1 * G.2^6 * G.3^-2 * G.2^8 * G.3^-2 ] Genus 35 action of group of order 154 via triangle group [ 2, 22, 77 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-4 * G.3^5 ] Genus 35 action of group of order 142 via triangle group [ 2, 71, 142 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^57 * G.2^-12 * G.3 ] Genus 35 action of group of order 144 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^58 * G.2^-13 ] Genus 35 action of group of order 144 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-11 * G.2^23 * G.3^-1 ] Genus 35 action of group of order 140 via triangle group [ 2, 140, 140 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^56 * G.2^-12 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^3 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 35 action of group of order 272 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 35 action of group of order 204 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 ] Genus 35 action of group of order 204 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 35 action of group of order 144 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-8 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 ] Genus 35 action of group of order 144 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-8 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-4 ] Genus 35 action of group of order 144 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^23 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 35 action of group of order 144 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-13 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 35 action of group of order 140 via triangle group [ 4, 4, 70 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^22 * G.2 * G.1^-1 * G.3^12 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 35 action of group of order 272 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 35 action of group of order 204 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-36 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-29 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-21 * G.1 * G.2 * G.1 * G.2 * G.4^-13 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-10 * G.2 * G.4 * G.1^2 * G.4 * G.3 * G.4^-3 * G.2 * G.4 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-12 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-11 * G.1 * G.2 * G.1 * G.4^4 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^8 * G.3 * G.1 * G.4^-8 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-9 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.4^5 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-11 * G.1 * G.2 * G.4^5 * G.3 * G.4^-1 ] Genus 35 action of group of order 144 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 35 action of group of order 140 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-17 * G.2 * G.3 * G.4^-17 ] Genus 35 action of group of order 140 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-28 * G.1 * G.3 * G.4^-6 ] Genus 35 action of group of order 140 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-28 * G.1 * G.2 * G.4^-6 ] Largest orientation-preserving group for genus 35 has order 544 ... group action with signature (0: +; [2,4,8]; {-}) Largest group with or without reflections for genus 35 has order 576 ... group action with signature (0; +; [-]; {(2,4,72)}) Largest group with reflections for genus 35 has order 576 ... group action with signature (0; +; [-]; {(2,4,72)}) Largest chiral group for genus 35 has order 544 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 36 has order 272 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 198 : 136 chiral, 62 reflexible, with 25 non-orientable quotient actions Genus 36 actions: Genus 36 action of group of order 672 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 36 action of group of order 672 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 36 action of group of order 600 via triangle group [ 2, 3, 20 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3^11 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 ] Genus 36 action of group of order 392 via triangle group [ 2, 4, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-6 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-6 ] Genus 36 action of group of order 312 via triangle group [ 2, 4, 39 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-23 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 36 action of group of order 296 via triangle group [ 2, 4, 74 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-66 * G.1 * G.2 * G.3^-7 ] Genus 36 action of group of order 288 via triangle group [ 2, 4, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-64 * G.1 * G.2^-1 * G.3^-7 ] Genus 36 action of group of order 300 via triangle group [ 2, 5, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.3^-1 * G.2)^5 ] Genus 36 action of group of order 336 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 36 action of group of order 336 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 36 action of group of order 300 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^10 ] Genus 36 action of group of order 300 via triangle group [ 2, 6, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^10 ] Genus 36 action of group of order 228 via triangle group [ 2, 6, 38 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^26 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^5 ] Genus 36 action of group of order 208 via triangle group [ 2, 8, 26 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^10 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 36 action of group of order 200 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-2 * G.1 * G.3^8 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 36 action of group of order 200 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^10 ] Genus 36 action of group of order 200 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^7 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 36 action of group of order 180 via triangle group [ 2, 10, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^8 * G.2 * G.3^-3 * G.1 * G.3^6 ] Genus 36 action of group of order 196 via triangle group [ 2, 14, 14 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.3 * G.2 * G.1 * G.2^-6 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-3 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 36 action of group of order 196 via triangle group [ 2, 14, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3 * G.2^-9 * G.3, G.3^-8 * G.2^2 * G.1 * G.2^-1 * G.3^-5 ] Genus 36 action of group of order 196 via triangle group [ 2, 14, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-3 * G.3 * G.2^-3 * G.3, G.2^-14 ] Genus 36 action of group of order 168 via triangle group [ 2, 14, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1, G.2^-3 * G.3^3 * G.2^-5 * G.3^3 ] Genus 36 action of group of order 160 via triangle group [ 2, 20, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-4 * G.2^2 * G.3^-4 ] Genus 36 action of group of order 168 via triangle group [ 2, 21, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2^-3 * G.3^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 36 action of group of order 156 via triangle group [ 2, 26, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-1 * G.2^9 * G.3^-3 * G.2^9 * G.3^-2 * G.2 ] Genus 36 action of group of order 152 via triangle group [ 2, 38, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-13 * G.2^11 * G.3^-1 * G.2^12 ] Genus 36 action of group of order 156 via triangle group [ 2, 39, 39 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-35 * G.3 * G.2^-1 ] Genus 36 action of group of order 150 via triangle group [ 2, 50, 75 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-13 * G.3^2 * G.2^-8 * G.3 * G.2^-1 ] Genus 36 action of group of order 146 via triangle group [ 2, 73, 146 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^59 * G.2^-12 * G.3 ] Genus 36 action of group of order 148 via triangle group [ 2, 74, 74 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^60 * G.2^-13 ] Genus 36 action of group of order 144 via triangle group [ 2, 144, 144 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^58 * G.2^-12 * G.3 ] Genus 36 action of group of order 336 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 ] Genus 36 action of group of order 336 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1 ] Genus 36 action of group of order 300 via triangle group [ 3, 3, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^10 ] Genus 36 action of group of order 228 via triangle group [ 3, 3, 38 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-3 * G.1 * G.3^4 ] Genus 36 action of group of order 228 via triangle group [ 3, 3, 38 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^4 ] Genus 36 action of group of order 219 via triangle group [ 3, 3, 73 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 36 action of group of order 219 via triangle group [ 3, 3, 73 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^4 * G.2 * G.1 * G.3^4 ] Genus 36 action of group of order 147 via triangle group [ 3, 7, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^3 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^-7 ] Genus 36 action of group of order 147 via triangle group [ 3, 7, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^3 * G.1^-1 * G.2^-1 * G.3^2, G.2^-7 ] Genus 36 action of group of order 150 via triangle group [ 3, 10, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 36 action of group of order 150 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, (G.2 * G.3^-1 * G.2)^2, G.2^3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^3 ] Genus 36 action of group of order 150 via triangle group [ 3, 10, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-3 ] Genus 36 action of group of order 150 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.2)^3, G.2^10 ] Genus 36 action of group of order 196 via triangle group [ 4, 4, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 36 action of group of order 148 via triangle group [ 4, 4, 37 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^24 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 36 action of group of order 148 via triangle group [ 4, 4, 37 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.2 * G.1 * G.3^-3 ] Genus 36 action of group of order 148 via triangle group [ 4, 4, 37 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.2 * G.1 * G.3^3 ] Genus 36 action of group of order 144 via triangle group [ 4, 4, 72 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^23 * G.2 * G.1^-1 * G.3^12 ] Genus 36 action of group of order 168 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 36 action of group of order 168 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 36 action of group of order 168 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 36 action of group of order 168 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 36 action of group of order 150 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 36 action of group of order 150 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^2 * G.1^-1 * G.3^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 36 action of group of order 196 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7 ] Genus 36 action of group of order 196 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-7 ] Genus 36 action of group of order 196 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-7 ] Genus 36 action of group of order 148 via quadrangle group [ 2, 2, 2, 37 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-18 * G.2 * G.1 * G.3 * G.4^-18 ] Genus 36 action of group of order 148 via quadrangle group [ 2, 2, 2, 37 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-30 * G.1^2 * G.4^-7 ] Genus 36 action of group of order 148 via quadrangle group [ 2, 2, 2, 37 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^23 * G.1^2 * G.4^14 ] Genus 36 action of group of order 144 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-18 * G.1 * G.4^-18 ] Genus 36 action of group of order 144 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-29 * G.2 * G.1^2 * G.4^-7 ] Genus 36 action of group of order 144 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-21 * G.1 * G.2 * G.4^-14 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.3 * G.4^-1)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.2 * G.1)^3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.2 * G.1 * G.4 * G.3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.3)^3 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.1)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4, G.4^-5 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^2 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-2 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1, (G.3 * G.2^-1)^3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.1 * G.2^-1 * G.4^2, (G.3 * G.2^-1)^3 ] Genus 36 action of group of order 168 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.4^-5 ] Genus 36 action of group of order 150 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-5 ] Largest orientation-preserving group for genus 36 has order 672 ... group action with signature (0: +; [2,3,16]; {-}) Largest group with or without reflections for genus 36 has order 1344 ... group action with signature (0; +; [-]; {(2,3,16)}) Largest group with reflections for genus 36 has order 1344 ... group action with signature (0; +; [-]; {(2,3,16)}) Largest chiral group for genus 36 has order 168 ... group action with signature (0: +; [4,6,6]; {-}) ... group action with signature (0; +; [2,2,3,4]; {-}) ... group action with signature (0; +; [2,3,2,4]; {-}) Largest non-orientable group for non-orientable genus 37 has order 392 ... group action with signature (0; +; [-]; {(2,4,14)}) Check total 100 : 26 chiral, 74 reflexible, with 24 non-orientable quotient actions Genus 37 actions: Genus 37 action of group of order 1728 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 ] Genus 37 action of group of order 1728 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 864 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 720 via triangle group [ 2, 3, 15 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^-5 * G.1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-9 ] Genus 37 action of group of order 648 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 37 action of group of order 648 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^6 * G.2 * G.1 * G.2^-2 * G.3^-4 * G.1, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 37 action of group of order 576 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 576 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^7 ] Genus 37 action of group of order 576 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-2 * G.1 * G.3^7 ] Genus 37 action of group of order 864 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^3 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 37 action of group of order 576 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3 ] Genus 37 action of group of order 480 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 432 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2^-1 * G.3)^6, G.3^-12 ] Genus 37 action of group of order 432 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, (G.2^-1 * G.3)^6 ] Genus 37 action of group of order 432 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2^-1 * G.3)^6, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 432 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3, (G.2^-1 * G.3)^6 ] Genus 37 action of group of order 360 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2^-1 * G.3)^6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 37 action of group of order 320 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-26 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-5 ] Genus 37 action of group of order 320 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-3 * G.1 * G.3^10 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 37 action of group of order 304 via triangle group [ 2, 4, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-68 * G.1 * G.2 * G.3^-7 ] Genus 37 action of group of order 296 via triangle group [ 2, 4, 148 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-66 * G.1 * G.2^-1 * G.3^-7 ] Genus 37 action of group of order 432 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 432 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 432 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^12 ] Genus 37 action of group of order 288 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6 ] Genus 37 action of group of order 270 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.3^2 ] Genus 37 action of group of order 240 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 37 action of group of order 234 via triangle group [ 2, 6, 39 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^13 * G.2 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.3^8 ] Genus 37 action of group of order 222 via triangle group [ 2, 6, 111 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^17 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2^-1 * G.3^-8 * G.1 * G.3 ] Genus 37 action of group of order 288 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 288 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, (G.2^-1 * G.3)^6 ] Genus 37 action of group of order 288 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 37 action of group of order 288 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3 ] Genus 37 action of group of order 216 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 240 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 216 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 37 action of group of order 192 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^2 ] Genus 37 action of group of order 192 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 37 action of group of order 192 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 37 action of group of order 192 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12 ] Genus 37 action of group of order 180 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^5 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 37 action of group of order 168 via triangle group [ 2, 21, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-7 * G.2^11 * G.3^-1 ] Genus 37 action of group of order 162 via triangle group [ 2, 27, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-1 * G.2^10 * G.3^-15 ] Genus 37 action of group of order 160 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-14 * G.2^11 * G.3^-1 * G.2^12 * G.3^-1 ] Genus 37 action of group of order 160 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^6 * G.3^-1 * G.2^8 * G.3^-2 ] Genus 37 action of group of order 150 via triangle group [ 2, 75, 150 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^61 * G.2^-12 * G.3 ] Genus 37 action of group of order 152 via triangle group [ 2, 76, 76 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^62 * G.2^-13 ] Genus 37 action of group of order 148 via triangle group [ 2, 148, 148 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^60 * G.2^-12 * G.3 ] Genus 37 action of group of order 864 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 37 action of group of order 864 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 37 action of group of order 864 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 37 action of group of order 864 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 432 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, (G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2)^2 ] Genus 37 action of group of order 324 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, (G.1^-1 * G.3^3 * G.2)^2 ] Genus 37 action of group of order 324 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 37 action of group of order 324 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 37 action of group of order 324 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3 * G.2)^2 ] Genus 37 action of group of order 288 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 37 action of group of order 252 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.1^-1 * G.3)^3 ] Genus 37 action of group of order 252 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, (G.2 * G.1^-1 * G.3)^3 ] Genus 37 action of group of order 432 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 37 action of group of order 432 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 37 action of group of order 432 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 180 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 37 action of group of order 180 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^2 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, (G.3^-1 * G.2)^3 ] Genus 37 action of group of order 216 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6 ] Genus 37 action of group of order 192 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 37 action of group of order 168 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 37 action of group of order 168 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 162 via triangle group [ 3, 6, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 37 action of group of order 162 via triangle group [ 3, 6, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 37 action of group of order 162 via triangle group [ 3, 6, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 37 action of group of order 162 via triangle group [ 3, 6, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 37 action of group of order 162 via triangle group [ 3, 6, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.3^-1 * G.1)^6 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-1)^6 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 37 action of group of order 288 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.1^-1 ] Genus 37 action of group of order 240 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 37 action of group of order 240 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 37 action of group of order 240 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 37 action of group of order 216 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 37 action of group of order 216 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 37 action of group of order 216 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 37 action of group of order 216 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 37 action of group of order 180 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-11 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.3 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.3^2 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2 * G.3^-4 * G.1^-1 * G.2^-1 * G.3^-7 * G.1 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 37 action of group of order 160 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 37 action of group of order 152 via triangle group [ 4, 4, 38 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^25 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 37 action of group of order 148 via triangle group [ 4, 4, 74 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^24 * G.2 * G.1^-1 * G.3^12 ] Genus 37 action of group of order 160 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 160 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.2 * G.4^-1)^6 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.4^-1)^6 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 432 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^18 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^18 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^12 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^18 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.3 * G.1)^9 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.1 * G.4^-2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 37 action of group of order 288 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-5, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-5, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-5, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-5, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-5, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 37 action of group of order 240 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.3 * G.1)^9 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^18 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.3 * G.4^-2 * G.1 * G.4^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.4 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.4 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 192 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^5 * G.3 * G.2 * G.4 * G.3 * G.4^-2 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 180 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, (G.2 * G.1)^12 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-7 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-7 * G.1 * G.2 * G.4^5 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-14 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^10 * G.1^2 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 * G.1^2 * G.4^4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^7 * G.1^2 * G.4^7 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^2 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^2 ] Genus 37 action of group of order 168 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-20 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-20 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^9 * G.3 * G.1 * G.3 * G.4^-5 * G.1 * G.4^4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^4 * G.2 * G.1 * G.4^6 * G.3 * G.1 * G.4^-1 * G.1 * G.4^8 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^10 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-7 * G.1 * G.2 * G.1 * G.4^7 * G.2 * G.4^-4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^11 * G.3 * G.4^-1 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^16 * G.1^2 * G.4^4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-12 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-5 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-5 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^5 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-5 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 160 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4 * G.3 * G.4^-6 * G.2 * G.4^5 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^7 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-2 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-6 * G.2 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-3 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 * G.3 * G.1 * G.4 * G.1^2 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 * G.3 * G.1 * G.4^4 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 37 action of group of order 156 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^3 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-13 * G.2 * G.4^4 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-14 * G.1 * G.4^-5 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-14 * G.1 * G.3 * G.4^-4 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^12 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-12 * G.1 * G.4^5 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-13 * G.1 * G.4^5 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-38 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-31 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 37 action of group of order 152 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^24 * G.1^2 * G.4^14 ] Genus 37 action of group of order 148 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-18 * G.2 * G.3 * G.4^-18 ] Genus 37 action of group of order 148 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-30 * G.1 * G.3 * G.4^-6 ] Genus 37 action of group of order 148 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^22 * G.2 * G.1 * G.4^14 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3 * G.1 * G.3^-1 * G.1)^6, G.2 * G.1^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.1^2 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^12, G.2 * G.1^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.1 * G.3^-1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.2^-1 * G.4^-1)^6, G.3 * G.1^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^6 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.3 * G.1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-1)^6, G.3 * G.1^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.4^-1 * G.2^-1)^3 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 37 action of group of order 216 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Largest orientation-preserving group for genus 37 has order 1728 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 37 has order 1728 ... group action with signature (0: +; [2,3,8]; {-}) ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) ... group action with signature (0; +; [-]; {(3,3,4)}) Largest group with reflections for genus 37 has order 1728 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) ... group action with signature (0; +; [-]; {(3,3,4)}) Largest chiral group for genus 37 has order 1728 ... group action with signature (0: +; [2,3,8]; {-}) Largest non-orientable group for non-orientable genus 38 has order 480 ... group action with signature (0; +; [-]; {(2,4,10)}) Check total 1459 : 816 chiral, 643 reflexible, with 149 non-orientable quotient actions Genus 38 actions: Genus 38 action of group of order 312 via triangle group [ 2, 4, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-70 * G.1 * G.2 * G.3^-7 ] Genus 38 action of group of order 304 via triangle group [ 2, 4, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-68 * G.1 * G.2^-1 * G.3^-7 ] Genus 38 action of group of order 444 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 38 action of group of order 444 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 38 action of group of order 444 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 38 action of group of order 444 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 38 action of group of order 240 via triangle group [ 2, 6, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^40 ] Genus 38 action of group of order 228 via triangle group [ 2, 6, 114 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^13 * G.2 * G.1 * G.3^14 * G.2 * G.3^-8 * G.1 * G.3 ] Genus 38 action of group of order 240 via triangle group [ 2, 8, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 38 action of group of order 208 via triangle group [ 2, 8, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^10 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 ] Genus 38 action of group of order 190 via triangle group [ 2, 10, 95 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^8 * G.2 * G.1 * G.2 * G.3^-5 * G.1 * G.3^4 ] Genus 38 action of group of order 192 via triangle group [ 2, 12, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-6 ] Genus 38 action of group of order 168 via triangle group [ 2, 28, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1, (G.2^-3 * G.3^3 * G.2^-1)^2 ] Genus 38 action of group of order 154 via triangle group [ 2, 77, 154 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^63 * G.2^-12 * G.3 ] Genus 38 action of group of order 156 via triangle group [ 2, 78, 78 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^64 * G.2^-13 ] Genus 38 action of group of order 152 via triangle group [ 2, 152, 152 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^62 * G.2^-12 * G.3 ] Genus 38 action of group of order 222 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 38 action of group of order 222 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 38 action of group of order 222 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 38 action of group of order 222 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 38 action of group of order 156 via triangle group [ 4, 4, 39 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.3^-1 ] Genus 38 action of group of order 156 via triangle group [ 4, 4, 39 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^26 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 38 action of group of order 156 via triangle group [ 4, 4, 39 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-2 * G.3^2 * G.2 ] Genus 38 action of group of order 152 via triangle group [ 4, 4, 76 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^25 * G.2 * G.1^-1 * G.3^12 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-6 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-5 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-6 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.1^2 * G.4^5 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^6 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.4^6 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-19 * G.2 * G.1 * G.3 * G.4^-19 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-32 * G.1^2 * G.4^-7 ] Genus 38 action of group of order 156 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-24 * G.1 * G.2 * G.1 * G.2 * G.4^-13 ] Genus 38 action of group of order 152 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-19 * G.1 * G.4^-19 ] Genus 38 action of group of order 152 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-31 * G.2 * G.1^2 * G.4^-7 ] Genus 38 action of group of order 152 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^23 * G.2 * G.1 * G.4^14 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.2 * G.4 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 38 action of group of order 222 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.2 ] Largest orientation-preserving group for genus 38 has order 444 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 38 has order 624 ... group action with signature (0; +; [-]; {(2,4,78)}) Largest group with reflections for genus 38 has order 624 ... group action with signature (0; +; [-]; {(2,4,78)}) Largest chiral group for genus 38 has order 444 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 39 has order 222 ... group action with signature (0; +; [2,3]; {(1)}) Check total 188 : 152 chiral, 36 reflexible, with 8 non-orientable quotient actions Genus 39 actions: Genus 39 action of group of order 912 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 39 action of group of order 912 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 39 action of group of order 336 via triangle group [ 2, 4, 42 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-26 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 39 action of group of order 320 via triangle group [ 2, 4, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-26 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 39 action of group of order 320 via triangle group [ 2, 4, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-72 * G.1 * G.2 * G.3^-7 ] Genus 39 action of group of order 312 via triangle group [ 2, 4, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-70 * G.1 * G.2^-1 * G.3^-7 ] Genus 39 action of group of order 288 via triangle group [ 2, 8, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 39 action of group of order 224 via triangle group [ 2, 8, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^16 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^5 ] Genus 39 action of group of order 224 via triangle group [ 2, 8, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-4 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-8 ] Genus 39 action of group of order 208 via triangle group [ 2, 8, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-7 * G.1 * G.3^8 * G.2 * G.1 * G.2^-1 * G.3^-9 ] Genus 39 action of group of order 208 via triangle group [ 2, 8, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-5 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 39 action of group of order 240 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^2 * G.2^3 * G.1 * G.3 * G.2^-1 ] Genus 39 action of group of order 192 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^12 ] Genus 39 action of group of order 192 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^9 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 39 action of group of order 182 via triangle group [ 2, 14, 91 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-5 ] Genus 39 action of group of order 192 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^6 * G.2 * G.3^-5 * G.1 ] Genus 39 action of group of order 192 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 39 action of group of order 168 via triangle group [ 2, 28, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-2 * G.2^10 * G.3^-3 * G.2^12 * G.3^-1 ] Genus 39 action of group of order 168 via triangle group [ 2, 42, 42 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-38 * G.3 * G.2^-1 ] Genus 39 action of group of order 158 via triangle group [ 2, 79, 158 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^65 * G.2^-12 * G.3 ] Genus 39 action of group of order 160 via triangle group [ 2, 80, 80 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^66 * G.2^-13 ] Genus 39 action of group of order 160 via triangle group [ 2, 80, 80 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-14 * G.2^11 * G.3^-1 * G.2^11 * G.3^-1 * G.2 ] Genus 39 action of group of order 156 via triangle group [ 2, 156, 156 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^64 * G.2^-12 * G.3 ] Genus 39 action of group of order 456 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 456 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 39 action of group of order 237 via triangle group [ 3, 3, 79 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 39 action of group of order 237 via triangle group [ 3, 3, 79 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.1 ] Genus 39 action of group of order 240 via triangle group [ 3, 4, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 39 action of group of order 228 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.3^2 * G.2 * G.1 ] Genus 39 action of group of order 228 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-2 * G.3 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^3 * G.3^-1 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.2^-1 * G.3^2, G.3 * G.2^2 * G.1^-1 * G.2^2 * G.1 ] Genus 39 action of group of order 171 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 39 action of group of order 168 via triangle group [ 4, 4, 21 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-15 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-3 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^33 * G.2 * G.1 * G.3^6 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-12 * G.1 * G.3 * G.2 * G.3^-6 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-11 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-6 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^6 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-12 * G.1 * G.2^-1 * G.3^-7 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^7 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.3^-7 * G.1 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 39 action of group of order 160 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 39 action of group of order 156 via triangle group [ 4, 4, 78 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^26 * G.2 * G.1^-1 * G.3^12 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 39 action of group of order 304 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 39 action of group of order 228 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-10 * G.2 * G.4^4 * G.3 * G.4^-6 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^10 * G.3 * G.2 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-10 * G.2 * G.1 * G.3 * G.4^-10 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^10 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^3 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^15 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-9 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^9 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^12 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 39 action of group of order 168 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^10 * G.2 * G.1 * G.4^5 * G.2 * G.1 * G.4^4 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-40 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-33 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^19 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^14 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-12 * G.2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-10 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-9 * G.1 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-10 * G.1 * G.4^-1 * G.1 * G.4^-9 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^10 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^6 * G.2 * G.4^-2 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 * G.3 * G.1 * G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^3 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.4^8 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^4 * G.3 * G.1 * G.4^-5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-3 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^5 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-5 * G.1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4^2 * G.3 * G.1 * G.4^6 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 160 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 39 action of group of order 156 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-19 * G.2 * G.3 * G.4^-19 ] Genus 39 action of group of order 156 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-32 * G.1 * G.3 * G.4^-6 ] Genus 39 action of group of order 156 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-24 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-9 ] Largest orientation-preserving group for genus 39 has order 912 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 39 has order 912 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 39 has order 672 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest chiral group for genus 39 has order 912 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 40 has order 336 ... group action with signature (0; +; [-]; {(2,4,42)}) Check total 242 : 142 chiral, 100 reflexible, with 34 non-orientable quotient actions Genus 40 actions: Genus 40 action of group of order 936 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 936 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 360 via triangle group [ 2, 4, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.1 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 40 action of group of order 328 via triangle group [ 2, 4, 82 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-74 * G.1 * G.2 * G.3^-7 ] Genus 40 action of group of order 320 via triangle group [ 2, 4, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-72 * G.1 * G.2^-1 * G.3^-7 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3^2 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 40 action of group of order 468 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 40 action of group of order 312 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 40 action of group of order 312 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 312 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 40 action of group of order 312 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 288 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-6 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 40 action of group of order 252 via triangle group [ 2, 6, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 40 action of group of order 252 via triangle group [ 2, 6, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^31 * G.2 * G.3^-8 * G.1 * G.3^2 ] Genus 40 action of group of order 252 via triangle group [ 2, 6, 42 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^15 * G.2 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2 * G.3^-9 * G.1 * G.3^6 ] Genus 40 action of group of order 240 via triangle group [ 2, 6, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-14 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-1 ] Genus 40 action of group of order 336 via triangle group [ 2, 7, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.3^8, (G.3 * G.2^-1 * G.3)^3 ] Genus 40 action of group of order 336 via triangle group [ 2, 7, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 40 action of group of order 234 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 40 action of group of order 234 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 40 action of group of order 216 via triangle group [ 2, 9, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 40 action of group of order 220 via triangle group [ 2, 10, 22 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^7 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 ] Genus 40 action of group of order 216 via triangle group [ 2, 12, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^5 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 40 action of group of order 216 via triangle group [ 2, 12, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^10 * G.2 * G.1 * G.2 * G.3^-4 * G.1 * G.3^2 ] Genus 40 action of group of order 216 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.2^-2 * G.3^4 ] Genus 40 action of group of order 216 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.3^2 ] Genus 40 action of group of order 192 via triangle group [ 2, 12, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^-9 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 40 action of group of order 180 via triangle group [ 2, 18, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-7 * G.3^3 * G.2^-5 * G.3^3 ] Genus 40 action of group of order 176 via triangle group [ 2, 22, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-11 * G.3^3 * G.2^-5 * G.3^3 ] Genus 40 action of group of order 180 via triangle group [ 2, 30, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-4 * G.2^10 * G.3^-14 * G.2 ] Genus 40 action of group of order 180 via triangle group [ 2, 30, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-3 * G.2^10 * G.3^-3 * G.2^14 ] Genus 40 action of group of order 180 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^7 * G.3^-1 * G.2 * G.3^-1 ] Genus 40 action of group of order 170 via triangle group [ 2, 34, 85 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1, G.2^-6 * G.3^3 * G.2^-6 * G.3^2 ] Genus 40 action of group of order 168 via triangle group [ 2, 42, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-16 * G.2^11 * G.3^-1 * G.2^11 * G.3^-1 * G.2 ] Genus 40 action of group of order 162 via triangle group [ 2, 81, 162 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^67 * G.2^-12 * G.3 ] Genus 40 action of group of order 164 via triangle group [ 2, 82, 82 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^14 * G.3^-68 ] Genus 40 action of group of order 160 via triangle group [ 2, 160, 160 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^66 * G.2^-12 * G.3 ] Genus 40 action of group of order 468 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 40 action of group of order 468 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 40 action of group of order 252 via triangle group [ 3, 3, 42 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^5 ] Genus 40 action of group of order 252 via triangle group [ 3, 3, 42 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2 * G.3^-1 * G.1 * G.3^5 ] Genus 40 action of group of order 360 via triangle group [ 3, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2 ] Genus 40 action of group of order 360 via triangle group [ 3, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1^-1 * G.3 * G.2 * G.3^-1 * G.2)^2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 40 action of group of order 234 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 ] Genus 40 action of group of order 180 via triangle group [ 3, 6, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3^2 ] Genus 40 action of group of order 180 via triangle group [ 3, 6, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 40 action of group of order 168 via triangle group [ 3, 6, 28 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 40 action of group of order 168 via triangle group [ 3, 6, 28 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^3 ] Genus 40 action of group of order 180 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 40 action of group of order 180 via triangle group [ 4, 4, 15 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 40 action of group of order 180 via triangle group [ 4, 4, 15 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 40 action of group of order 164 via triangle group [ 4, 4, 41 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^-3 * G.2 ] Genus 40 action of group of order 164 via triangle group [ 4, 4, 41 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-28 * G.1^-1 * G.2^-1 * G.3^-12 ] Genus 40 action of group of order 164 via triangle group [ 4, 4, 41 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.2^-1 * G.1 * G.3^-3 * G.2 ] Genus 40 action of group of order 160 via triangle group [ 4, 4, 80 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^33 * G.2 * G.1^-1 * G.3^6 ] Genus 40 action of group of order 168 via triangle group [ 4, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, (G.2^-1 * G.1)^3, (G.3^-1 * G.1)^3 ] Genus 40 action of group of order 168 via triangle group [ 4, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, (G.2 * G.3^-1 * G.2)^2, G.2^3 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 312 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^3 * G.1 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-2 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^6 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^7 * G.2 * G.1 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^3 * G.3 * G.4^-3 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^8 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^3 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 ] Genus 40 action of group of order 180 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 164 via quadrangle group [ 2, 2, 2, 41 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-20 * G.2 * G.1 * G.3 * G.4^-20 ] Genus 40 action of group of order 164 via quadrangle group [ 2, 2, 2, 41 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-34 * G.1^2 * G.4^-7 ] Genus 40 action of group of order 164 via quadrangle group [ 2, 2, 2, 41 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^25 * G.2 * G.1 * G.2 * G.1 * G.4^14 ] Genus 40 action of group of order 160 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-20 * G.1 * G.4^-20 ] Genus 40 action of group of order 160 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-33 * G.2 * G.1^2 * G.4^-7 ] Genus 40 action of group of order 160 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^19 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^13 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 40 action of group of order 234 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Largest orientation-preserving group for genus 40 has order 936 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 40 has order 936 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 40 has order 720 ... group action with signature (0; +; [-]; {(3,4,5)}) ... group action with signature (0; +; [-]; {(2,4,30)}) Largest chiral group for genus 40 has order 936 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 41 has order 360 ... group action with signature (0; +; [-]; {(3,4,5)}) Check total 369 : 290 chiral, 79 reflexible, with 22 non-orientable quotient actions Genus 41 actions: Genus 41 action of group of order 768 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^7 ] Genus 41 action of group of order 768 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 960 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.2 * G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.3^-1 * G.2)^5, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.2 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.3^-1 * G.2)^5, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-3 * G.2 * G.3^-1 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 640 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-4 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-12, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-12, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 480 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^3, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 41 action of group of order 400 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-5 * G.2 ] Genus 41 action of group of order 400 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^8 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 41 action of group of order 400 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.1 * G.3^7 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-8 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-10 * G.1 * G.3^7 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 360 via triangle group [ 2, 4, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-9 ] Genus 41 action of group of order 360 via triangle group [ 2, 4, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^5 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 352 via triangle group [ 2, 4, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-29 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 41 action of group of order 336 via triangle group [ 2, 4, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-76 * G.1 * G.2 * G.3^-7 ] Genus 41 action of group of order 328 via triangle group [ 2, 4, 164 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-74 * G.1 * G.2^-1 * G.3^-7 ] Genus 41 action of group of order 600 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 600 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 41 action of group of order 480 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^8, (G.2 * G.3^-1 * G.2)^4 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^8 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 ] Genus 41 action of group of order 384 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 41 action of group of order 264 via triangle group [ 2, 6, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^5 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 41 action of group of order 246 via triangle group [ 2, 6, 123 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-15 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-3 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.2 * G.3^-2 * G.2^3 * G.3^-3 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^8 * G.2 * G.3^-6 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^-2 * G.1 * G.2^-3 * G.3^-5 ] Genus 41 action of group of order 256 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.2^-3 * G.3^-5 ] Genus 41 action of group of order 240 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 41 action of group of order 240 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 240 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 224 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 224 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^16 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^4 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-5 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3 * G.2^-2 * G.3^-1 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^12 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 ] Genus 41 action of group of order 240 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 224 via triangle group [ 2, 14, 14 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-14 ] Genus 41 action of group of order 224 via triangle group [ 2, 14, 14 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-14 ] Genus 41 action of group of order 192 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-5 * G.3^2 * G.2^-7 * G.3^2, G.3^4 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-5 * G.3^2 * G.2^-7 * G.3^2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^4 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 41 action of group of order 200 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, (G.2^-8 * G.3 * G.2^-1)^2 ] Genus 41 action of group of order 200 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2^8 * G.3^-4 ] Genus 41 action of group of order 200 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^9 * G.3^-3 * G.2 ] Genus 41 action of group of order 200 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2^-1 * G.3^2 * G.2^-1 * G.3^4 * G.2^-9 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 200 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-5 * G.3^-5 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-10 * G.2^9 * G.3^-2 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-8 * G.3 * G.2^-2 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^7 * G.3^-2 * G.2 * G.3^-2 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-12 * G.3^2 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^10 * G.3^-1 * G.2^7 * G.3^-2 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3^10 * G.2^-1 * G.3 * G.2^-10 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2^6 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^9 * G.3^-1 * G.2 * G.3^-1 ] Genus 41 action of group of order 180 via triangle group [ 2, 36, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^7 * G.3^-5 ] Genus 41 action of group of order 180 via triangle group [ 2, 36, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2^8 * G.3^-5 ] Genus 41 action of group of order 176 via triangle group [ 2, 44, 44 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-17 * G.2^11 * G.3^-1 * G.2^14 ] Genus 41 action of group of order 166 via triangle group [ 2, 83, 166 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^68 * G.2^-14 ] Genus 41 action of group of order 168 via triangle group [ 2, 84, 84 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^15 * G.3^-68 * G.2 ] Genus 41 action of group of order 164 via triangle group [ 2, 164, 164 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^14 * G.3^-67 * G.2 ] Genus 41 action of group of order 384 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^8 ] Genus 41 action of group of order 384 via triangle group [ 3, 3, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 384 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3^8, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 384 via triangle group [ 3, 3, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 41 action of group of order 480 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^-4 ] Genus 41 action of group of order 240 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 41 action of group of order 300 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 300 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2^3 * G.1^-1 * G.3^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2^3 * G.1^-1 * G.3^3, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.2^3 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^8, G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^8, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^8, G.2 * G.3^-1 * G.2^3 * G.1^-1 * G.2^-1 * G.3^4 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, (G.3^-1 * G.2)^3, G.2^8 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2, G.2^8 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^8 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2^3 * G.1^-1 * G.3^3, G.2^8 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.3^2 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 240 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.2^-1 * G.3^2 * G.1^-1 * G.2 * G.3^-2 * G.1 * G.3 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^10 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^10 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^10 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 41 action of group of order 200 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-5 * G.1^-1 * G.3^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^12 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3 * G.2^-1 * G.3^-5 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.3^-1)^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3^3, (G.2 * G.3^-1)^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-5 * G.1 * G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3^-6 * G.1^-1 * G.3^5 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.1 * G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-7 * G.1 * G.2 * G.3^-4 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^12 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3 * G.2 * G.3^-5 * G.1^-1 * G.3^5 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^12 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3 * G.2^-1 * G.3^-5 * G.1^-1 * G.2 * G.3^-4 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-6 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-7 * G.1 * G.2 * G.3^-4 ] Genus 41 action of group of order 180 via triangle group [ 4, 4, 18 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 41 action of group of order 180 via triangle group [ 4, 4, 18 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 176 via triangle group [ 4, 4, 22 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^10 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-6 * G.1 ] Genus 41 action of group of order 168 via triangle group [ 4, 4, 42 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-29 * G.1^-1 * G.2^-1 * G.3^-12 ] Genus 41 action of group of order 164 via triangle group [ 4, 4, 82 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-28 * G.1^-1 * G.2 * G.3^-12 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.2^-2, G.2^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1, G.2^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.3^-1 * G.2)^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, (G.1 * G.3 * G.2)^2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.2 * G.3^-2)^2, G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^2, G.3^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.3^-1 * G.1)^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^6, G.3 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.3^-1 * G.1)^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3 ] Genus 41 action of group of order 192 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2^6 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 480 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^20 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^10 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^10 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^20 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^10 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.2 * G.1)^5 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.3 * G.1)^5 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^5, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 320 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^10 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^10 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.2 * G.1)^5 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.2 * G.4^-2 * G.1 * G.4)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, (G.4^-1 * G.2)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-6 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3)^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^6 * G.1^2 * G.4^4, (G.4^-1 * G.2)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.4^-1 * G.2)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.3 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.4^4 * G.3 * G.1 * G.4^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.3 * G.1)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^5 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^10, G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, (G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^6 * G.1^2 * G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-6 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 200 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-6 * G.1^2 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-3 * G.1 * G.2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4^5 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-6 * G.1 * G.2 * G.3 * G.4^-5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.3 * G.1 * G.4^3 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^6 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1^2 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.4^-5 * G.1 * G.2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^6 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-3 * G.2 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^4 * G.2 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^7 * G.3 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-8 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1^2 * G.4^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1, G.4^8 * G.1^2 * G.4^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-3 * G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^7 * G.1^2 * G.4^5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^6 * G.3 * G.1 * G.4^2 * G.2 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.4^-4 * G.2 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^4 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^3 * G.2 * G.4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 41 action of group of order 180 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4^5 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^8, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4^4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-6 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-22 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^9 * G.3 * G.4^-1 * G.1 * G.4^-9 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-6 * G.1 * G.4^4 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^4 * G.3 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^9 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^9 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-9 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^3 * G.3 * G.4^-7 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^22 ] Genus 41 action of group of order 176 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^22 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^10 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-7 * G.2 * G.4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^15 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-16 * G.1 * G.3 * G.4^-4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^14 * G.2 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-14 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 * G.1 * G.4^-1 * G.1 * G.4^-6 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^6 * G.3 * G.1 * G.4 * G.3 * G.4^-5 * G.1 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^7 * G.1 * G.4^-1 * G.1 * G.4^6 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-3 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-42 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-35 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 41 action of group of order 168 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-26 * G.1 * G.2 * G.1 * G.4^14 * G.2 ] Genus 41 action of group of order 164 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-20 * G.2 * G.3 * G.4^-20 ] Genus 41 action of group of order 164 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-34 * G.1 * G.3 * G.4^-6 ] Genus 41 action of group of order 164 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^26 * G.2 * G.1 * G.4^14 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.3^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, (G.3^-1 * G.1)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, (G.4^-1 * G.2)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.3 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.3 * G.4^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2, (G.2 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3^-1)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.4^-1 * G.3)^3, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.3^-1 * G.2 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 41 action of group of order 240 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2^-1)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.1 * G.2^-1)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.4^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.2 * G.4^-1 * G.1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1, (G.2^-1 * G.1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.3 * G.2^-1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2 * G.4^-1 * G.1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.2^-1)^3, (G.2 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.2^-1 * G.1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.3 * G.2^-1)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.4^-1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, (G.2 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, (G.2^-1 * G.1)^4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.2^-1 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.1)^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.3 * G.1)^3 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 41 action of group of order 192 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Largest orientation-preserving group for genus 41 has order 960 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 41 has order 1920 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 41 has order 1920 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 41 has order 640 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 42 has order 600 ... group action with signature (0; +; [-]; {(2,5,6)}) Check total 1498 : 814 chiral, 684 reflexible, with 209 non-orientable quotient actions Genus 42 actions: Genus 42 action of group of order 360 via triangle group [ 2, 4, 45 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-28 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 42 action of group of order 344 via triangle group [ 2, 4, 86 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-78 * G.1 * G.2 * G.3^-7 ] Genus 42 action of group of order 336 via triangle group [ 2, 4, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-76 * G.1 * G.2^-1 * G.3^-7 ] Genus 42 action of group of order 410 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 42 action of group of order 410 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 42 action of group of order 410 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^3 ] Genus 42 action of group of order 410 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 42 action of group of order 264 via triangle group [ 2, 6, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^17 * G.2 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2 * G.3^-9 * G.1 * G.3^6 ] Genus 42 action of group of order 328 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 42 action of group of order 328 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 42 action of group of order 328 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2 ] Genus 42 action of group of order 328 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 42 action of group of order 240 via triangle group [ 2, 8, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 42 action of group of order 240 via triangle group [ 2, 8, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^12 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-11 * G.1 * G.3^4 ] Genus 42 action of group of order 210 via triangle group [ 2, 10, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^3 * G.2 * G.3^-2 * G.1 * G.3^15 ] Genus 42 action of group of order 224 via triangle group [ 2, 14, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^4 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 42 action of group of order 182 via triangle group [ 2, 26, 91 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-2 * G.3^3 * G.2^-4 * G.3^4 ] Genus 42 action of group of order 176 via triangle group [ 2, 44, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-11 * G.3^3 * G.2^-6 * G.3 * G.2^-1 ] Genus 42 action of group of order 180 via triangle group [ 2, 45, 45 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-41 * G.3 * G.2^-1 ] Genus 42 action of group of order 174 via triangle group [ 2, 58, 87 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-1 * G.2^10 * G.3^-3 * G.2^13 * G.3^-1 ] Genus 42 action of group of order 170 via triangle group [ 2, 85, 170 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^69 * G.2^-14 * G.3 ] Genus 42 action of group of order 172 via triangle group [ 2, 86, 86 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^16 * G.3^-70 ] Genus 42 action of group of order 168 via triangle group [ 2, 168, 168 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^15 * G.3^-69 ] Genus 42 action of group of order 172 via triangle group [ 4, 4, 43 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^36 * G.2 * G.1 * G.3^6 ] Genus 42 action of group of order 168 via triangle group [ 4, 4, 84 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-29 * G.1^-1 * G.2 * G.3^-12 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.3^-1 * G.1^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.1^-2 * G.2^2 * G.1, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.2^-1 * G.3^2 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.2^-1 * G.3 * G.2 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.1 * G.3^-1 * G.1^-2 * G.2^-1 * G.3 * G.2^-1 ] Genus 42 action of group of order 205 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 ] Genus 42 action of group of order 172 via quadrangle group [ 2, 2, 2, 43 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-21 * G.2 * G.1 * G.3 * G.4^-21 ] Genus 42 action of group of order 172 via quadrangle group [ 2, 2, 2, 43 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-36 * G.1^2 * G.4^-7 ] Genus 42 action of group of order 172 via quadrangle group [ 2, 2, 2, 43 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-27 * G.1 * G.2 * G.1 * G.4^14 * G.2 ] Genus 42 action of group of order 168 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-21 * G.1 * G.4^-21 ] Genus 42 action of group of order 168 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-35 * G.2 * G.1^2 * G.4^-7 ] Genus 42 action of group of order 168 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-25 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^14 * G.2 ] Largest orientation-preserving group for genus 42 has order 410 ... group action with signature (0: +; [2,5,10]; {-}) Largest group with or without reflections for genus 42 has order 720 ... group action with signature (0; +; [-]; {(2,4,45)}) Largest group with reflections for genus 42 has order 720 ... group action with signature (0; +; [-]; {(2,4,45)}) Largest chiral group for genus 42 has order 410 ... group action with signature (0: +; [2,5,10]; {-}) Largest non-orientable group for non-orientable genus 43 has order 360 ... group action with signature (0; +; [-]; {(2,4,45)}) Check total 43 : 20 chiral, 23 reflexible, with 6 non-orientable quotient actions Genus 43 actions: Genus 43 action of group of order 1512 via triangle group [ 2, 3, 9 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 43 action of group of order 1512 via triangle group [ 2, 3, 9 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 1512 via triangle group [ 2, 3, 9 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 1008 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 43 action of group of order 1008 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 43 action of group of order 720 via triangle group [ 2, 3, 20 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 43 action of group of order 672 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 43 action of group of order 672 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 43 action of group of order 352 via triangle group [ 2, 4, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-30 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 43 action of group of order 352 via triangle group [ 2, 4, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-80 * G.1 * G.2 * G.3^-7 ] Genus 43 action of group of order 344 via triangle group [ 2, 4, 172 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-78 * G.1 * G.2^-1 * G.3^-7 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 378 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 43 action of group of order 336 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 43 action of group of order 336 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 43 action of group of order 294 via triangle group [ 2, 6, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^2 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 43 action of group of order 294 via triangle group [ 2, 6, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-1 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 288 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 43 action of group of order 288 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 43 action of group of order 288 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 43 action of group of order 288 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-3)^2 ] Genus 43 action of group of order 270 via triangle group [ 2, 6, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-16 * G.1 * G.3 * G.2 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 43 action of group of order 270 via triangle group [ 2, 6, 45 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 43 action of group of order 270 via triangle group [ 2, 6, 45 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-1 * G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 43 action of group of order 258 via triangle group [ 2, 6, 129 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^33 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 43 action of group of order 336 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^8, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 43 action of group of order 336 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, G.3^8, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 43 action of group of order 288 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3 ] Genus 43 action of group of order 288 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, (G.2^-1 * G.3)^6 ] Genus 43 action of group of order 240 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 43 action of group of order 240 via triangle group [ 2, 12, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.3^2 ] Genus 43 action of group of order 216 via triangle group [ 2, 12, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12 ] Genus 43 action of group of order 216 via triangle group [ 2, 12, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^-14 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 216 via triangle group [ 2, 12, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12 ] Genus 43 action of group of order 216 via triangle group [ 2, 12, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^4 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 43 action of group of order 210 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3^3 * G.2^-6 * G.3^3 * G.2^-1 ] Genus 43 action of group of order 210 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-8 * G.3^2 ] Genus 43 action of group of order 192 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2^-4 * G.3^5 ] Genus 43 action of group of order 192 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^9 * G.3^-1 * G.2 * G.3^-1 ] Genus 43 action of group of order 174 via triangle group [ 2, 87, 174 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^70 * G.2^-16 ] Genus 43 action of group of order 176 via triangle group [ 2, 88, 88 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^17 * G.3^-70 * G.2 ] Genus 43 action of group of order 176 via triangle group [ 2, 88, 88 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-18 * G.2^11 * G.3^-1 * G.2^13 * G.3^-1 ] Genus 43 action of group of order 172 via triangle group [ 2, 172, 172 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^16 * G.3^-69 * G.2 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 504 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 43 action of group of order 360 via triangle group [ 3, 3, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 43 action of group of order 336 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 336 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 336 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, (G.1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 43 action of group of order 336 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 43 action of group of order 252 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 43 action of group of order 252 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.2^-9 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-9 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 189 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 43 action of group of order 336 via triangle group [ 4, 4, 4 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 43 action of group of order 176 via triangle group [ 4, 4, 44 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^13 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-6 * G.1^-1 ] Genus 43 action of group of order 176 via triangle group [ 4, 4, 44 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^13 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-6 * G.1 ] Genus 43 action of group of order 176 via triangle group [ 4, 4, 44 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^44 ] Genus 43 action of group of order 176 via triangle group [ 4, 4, 44 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^10 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-6 * G.1^-1 ] Genus 43 action of group of order 172 via triangle group [ 4, 4, 86 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^36 * G.2 * G.1^-1 * G.3^6 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.4^-1 * G.2 * G.4)^3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 504 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1 * G.4)^3, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1 * G.4)^3, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^14 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^21 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 336 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^21 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 252 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, (G.1 * G.2 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 224 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 43 action of group of order 196 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^9 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-16 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.3 * G.4^-5 * G.1 * G.2 * G.4^6 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 * G.1^2 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^16 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^10 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.4^5 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 43 action of group of order 192 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^9 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.2 * G.4 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^7 * G.1 * G.3 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-7 * G.2 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-4 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^3 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 * G.3 * G.1 * G.4^4 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 * G.2 ] Genus 43 action of group of order 180 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-8 * G.1 * G.4^5 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-44 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-37 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^28 * G.2 * G.1 * G.2 * G.1 * G.4^14 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^9 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^15 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^6 * G.2 * G.1 * G.4^13 * G.2 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-11 * G.1 * G.4^-1 * G.1 * G.4^-10 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.4^12 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^5 * G.2 * G.1 * G.4^5 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^4 * G.3 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^8 ] Genus 43 action of group of order 176 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4^13 ] Genus 43 action of group of order 172 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-21 * G.2 * G.3 * G.4^-21 ] Genus 43 action of group of order 172 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-36 * G.1 * G.3 * G.4^-6 ] Genus 43 action of group of order 172 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-26 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^14 * G.2 ] Largest orientation-preserving group for genus 43 has order 1512 ... group action with signature (0: +; [2,3,9]; {-}) Largest group with or without reflections for genus 43 has order 3024 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest group with reflections for genus 43 has order 3024 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest chiral group for genus 43 has order 1512 ... group action with signature (0: +; [2,3,9]; {-}) Largest non-orientable group for non-orientable genus 44 has order 672 ... group action with signature (0; +; [-]; {(2,4,8)}) Check total 646 : 444 chiral, 202 reflexible, with 74 non-orientable quotient actions Genus 44 actions: Genus 44 action of group of order 360 via triangle group [ 2, 4, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-82 * G.1 * G.2 * G.3^-7 ] Genus 44 action of group of order 352 via triangle group [ 2, 4, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-80 * G.1 * G.2^-1 * G.3^-7 ] Genus 44 action of group of order 516 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 44 action of group of order 516 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 44 action of group of order 516 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 44 action of group of order 516 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 44 action of group of order 276 via triangle group [ 2, 6, 46 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-24 * G.1 * G.3^5 * G.2^-1 * G.3^-16 ] Genus 44 action of group of order 264 via triangle group [ 2, 6, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^17 * G.2 * G.1 * G.3^15 * G.2 * G.3^-8 * G.1 * G.3^2 ] Genus 44 action of group of order 240 via triangle group [ 2, 8, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^12 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^15 ] Genus 44 action of group of order 240 via triangle group [ 2, 10, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 44 action of group of order 220 via triangle group [ 2, 10, 110 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 44 action of group of order 198 via triangle group [ 2, 18, 99 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-5 ] Genus 44 action of group of order 184 via triangle group [ 2, 46, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-20 * G.2^11 * G.3^-1 * G.2^13 * G.3^-1 ] Genus 44 action of group of order 178 via triangle group [ 2, 89, 178 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^71 * G.2^-16 * G.3 ] Genus 44 action of group of order 180 via triangle group [ 2, 90, 90 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^18 * G.3^-72 ] Genus 44 action of group of order 176 via triangle group [ 2, 176, 176 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^17 * G.3^-71 ] Genus 44 action of group of order 258 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 44 action of group of order 258 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 44 action of group of order 258 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 44 action of group of order 258 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 44 action of group of order 180 via triangle group [ 4, 4, 45 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^45 ] Genus 44 action of group of order 180 via triangle group [ 4, 4, 45 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1 * G.3^6 ] Genus 44 action of group of order 180 via triangle group [ 4, 4, 45 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 44 action of group of order 176 via triangle group [ 4, 4, 88 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^31 * G.2^-1 * G.3^-4 * G.1 * G.3^8 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 * G.4^4 * G.3 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-4 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.4^3 * G.2 * G.4^-3 * G.1 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^4 * G.3 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-3 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-22 * G.2 * G.1 * G.3 * G.4^-22 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-38 * G.1^2 * G.4^-7 ] Genus 44 action of group of order 180 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^45 ] Genus 44 action of group of order 176 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-22 * G.1 * G.4^-22 ] Genus 44 action of group of order 176 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-37 * G.2 * G.1^2 * G.4^-7 ] Genus 44 action of group of order 176 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^28 * G.2 * G.1 * G.4^15 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 44 action of group of order 258 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Largest orientation-preserving group for genus 44 has order 516 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 44 has order 720 ... group action with signature (0; +; [-]; {(2,4,90)}) Largest group with reflections for genus 44 has order 720 ... group action with signature (0; +; [-]; {(2,4,90)}) Largest chiral group for genus 44 has order 516 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 45 has order 276 ... group action with signature (0; +; [-]; {(2,6,46)}) Check total 212 : 176 chiral, 36 reflexible, with 9 non-orientable quotient actions Genus 45 actions: Genus 45 action of group of order 1320 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2^2 * G.3^-3 * G.1 * G.3^2 ] Genus 45 action of group of order 1320 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3^3 ] Genus 45 action of group of order 726 via triangle group [ 2, 3, 22 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-21 * G.1 ] Genus 45 action of group of order 672 via triangle group [ 2, 3, 28 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 45 action of group of order 480 via triangle group [ 2, 4, 15 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2, G.3^-7 * G.1 * G.2 * G.3^-7 ] Genus 45 action of group of order 384 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-8 * G.1 * G.3^8 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 45 action of group of order 384 via triangle group [ 2, 4, 48 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-30 * G.1 * G.3^7 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-8 ] Genus 45 action of group of order 384 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-38 * G.1 * G.2 * G.3^-9 ] Genus 45 action of group of order 384 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-10 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 368 via triangle group [ 2, 4, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-84 * G.1 * G.2 * G.3^-7 ] Genus 45 action of group of order 360 via triangle group [ 2, 4, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-82 * G.1 * G.2^-1 * G.3^-7 ] Genus 45 action of group of order 660 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 45 action of group of order 660 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5 ] Genus 45 action of group of order 336 via triangle group [ 2, 6, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-2 * G.1 * G.2^-2 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 45 action of group of order 320 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^3 * G.1 * G.3^2, (G.2 * G.3^-1)^4 ] Genus 45 action of group of order 320 via triangle group [ 2, 8, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^3 * G.1 * G.3^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^8 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^22 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^8 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^10 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3^15 ] Genus 45 action of group of order 256 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 240 via triangle group [ 2, 8, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-1 * G.1 * G.3^17 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 45 action of group of order 240 via triangle group [ 2, 8, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-4 * G.1 * G.3^16 * G.2 * G.1 * G.2^-1 * G.3^-8 ] Genus 45 action of group of order 242 via triangle group [ 2, 11, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-11 ] Genus 45 action of group of order 240 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-20 ] Genus 45 action of group of order 240 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-1 * G.1 * G.2^-2 * G.3^-3, (G.3^-1 * G.2)^5 ] Genus 45 action of group of order 240 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-2 * G.2^3 * G.3^-3, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 ] Genus 45 action of group of order 210 via triangle group [ 2, 14, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^2 * G.2^-7 * G.3^2, G.3^-9 * G.2 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 45 action of group of order 240 via triangle group [ 2, 15, 15 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^2 * G.3^-1, G.2^-15 ] Genus 45 action of group of order 240 via triangle group [ 2, 15, 15 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.2^-15 ] Genus 45 action of group of order 240 via triangle group [ 2, 15, 15 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2^2, G.2^-15 ] Genus 45 action of group of order 198 via triangle group [ 2, 22, 99 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2^-2 * G.3^5 ] Genus 45 action of group of order 192 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-3 * G.2^11 * G.3^-2 * G.2^14 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-5 * G.3^2 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 45 action of group of order 190 via triangle group [ 2, 38, 95 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-7 * G.3 * G.2^-6 * G.3^4 * G.2^-1 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-32 * G.3 * G.2^-13 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-10 * G.2^11 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^9 * G.3^-3 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^7 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-21 * G.2^11 * G.3^-2 * G.2^13 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3^10 * G.2^-1 * G.3 * G.2^-8 * G.3 * G.2^-2 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^10 * G.3^-1 * G.2^8 * G.3^-2 ] Genus 45 action of group of order 192 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-12 * G.3^2 * G.2^-8 * G.3^2 ] Genus 45 action of group of order 186 via triangle group [ 2, 62, 93 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-4 * G.2^10 * G.3^-3 * G.2^12 * G.3^-2 ] Genus 45 action of group of order 182 via triangle group [ 2, 91, 182 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^72 * G.2^-18 ] Genus 45 action of group of order 184 via triangle group [ 2, 92, 92 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^19 * G.3^-72 * G.2 ] Genus 45 action of group of order 180 via triangle group [ 2, 180, 180 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^18 * G.3^-71 * G.2 ] Genus 45 action of group of order 660 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 45 action of group of order 660 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 45 action of group of order 363 via triangle group [ 3, 3, 11 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^4 ] Genus 45 action of group of order 336 via triangle group [ 3, 3, 14 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-3 * G.1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 45 action of group of order 273 via triangle group [ 3, 3, 91 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3^5 * G.1^-1 * G.3^-5 ] Genus 45 action of group of order 273 via triangle group [ 3, 3, 91 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1^-1 * G.3^8 * G.2^-1 * G.3^-1 ] Genus 45 action of group of order 273 via triangle group [ 3, 3, 91 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1 * G.3^9 * G.2 ] Genus 45 action of group of order 273 via triangle group [ 3, 3, 91 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1 * G.3^6 * G.1^-1 * G.3^-5 ] Genus 45 action of group of order 240 via triangle group [ 3, 4, 20 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2 * G.3^-3 * G.1 * G.3^-4 ] Genus 45 action of group of order 192 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3^-5 * G.1 * G.3^6 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.2 * G.3^-6 * G.1^-1 * G.3^5 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^4 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-18 * G.1 * G.2 * G.3^-5 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^6 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.2^-1 * G.3^-3 * G.1^-1 * G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^12 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.2 * G.3^-4 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^5 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-15 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.1 * G.3^4 * G.2 * G.1^-1 * G.3^4 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-18 * G.1 * G.2 * G.3^-5 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-7 * G.1 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-6 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-7 * G.1^-1 * G.3 * G.2 * G.3^-3 ] Genus 45 action of group of order 192 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-7 * G.1 * G.2^-1 * G.3^-4 ] Genus 45 action of group of order 184 via triangle group [ 4, 4, 46 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^46 ] Genus 45 action of group of order 180 via triangle group [ 4, 4, 90 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^32 * G.2^-1 * G.3^-4 * G.1 * G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, (G.3^-1 * G.1)^3, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, (G.3^-1 * G.1)^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, (G.1 * G.3^-2)^2, G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.2^2 * G.1^2 * G.2^-1 * G.3 * G.2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2^2 * G.1^-2 * G.3 * G.2 * G.1^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-2)^2, G.2^6, G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.3^-1 * G.1)^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2, (G.3^-1 * G.1)^3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1 * G.3^2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 45 action of group of order 192 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^22 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^22 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 352 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 45 action of group of order 264 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 220 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-24 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-4 * G.2 * G.4^4 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 * G.1^2 * G.4^12 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.2 * G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^12 * G.3 * G.4^-5 * G.1 * G.2 * G.4^6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-9 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-5 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.4^5 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^4 * G.3 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-3 * G.1^2 * G.2 * G.4^2 * G.3 * G.2 * G.4^2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.1^2 * G.3 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.3 * G.1 * G.4^5 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-7 * G.1 * G.2 * G.4^2 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^6 * G.2 * G.1 * G.4^5 * G.3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.2 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^8 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.1^2 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7 * G.1 * G.2 * G.4^2 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^5 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-5 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^2 * G.2 * G.4^4 * G.3 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-9 * G.2 * G.4^11 * G.3 * G.4^-1 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^20 * G.1^2 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^7 * G.2 * G.1 * G.4^15 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-5 * G.2 * G.3 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^5 * G.1^2 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-5 * G.2 * G.3 * G.1 * G.4^-6 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-5 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^6 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^6 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^17 * G.3 * G.4^-2 * G.1 * G.2 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-18 * G.2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-24 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^6 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^18 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^11 * G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-12 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-2 * G.1^2 * G.4^-2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^13 * G.2 * G.1 * G.4^5 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^12 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^18 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.1 * G.4)^3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 45 action of group of order 192 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-12 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^6 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^11 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^17 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-18 * G.1 * G.3 * G.4^-4 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^21 * G.2 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^22 * G.2 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-46 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-39 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 45 action of group of order 184 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-26 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-15 ] Genus 45 action of group of order 180 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-22 * G.2 * G.3 * G.4^-22 ] Genus 45 action of group of order 180 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-38 * G.1 * G.3 * G.4^-6 ] Genus 45 action of group of order 180 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^30 * G.2 * G.1 * G.4^14 ] Largest orientation-preserving group for genus 45 has order 1320 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 45 has order 2640 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 45 has order 2640 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 45 has order 352 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 46 has order 1320 ... group action with signature (0; +; [-]; {(2,3,10)}) Check total 564 : 268 chiral, 296 reflexible, with 73 non-orientable quotient actions Genus 46 actions: Genus 46 action of group of order 2160 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 46 action of group of order 2160 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 46 action of group of order 2160 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 46 action of group of order 2160 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 ] Genus 46 action of group of order 648 via triangle group [ 2, 3, 36 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-7 * G.1 ] Genus 46 action of group of order 720 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1, G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 ] Genus 46 action of group of order 720 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, (G.3^-2 * G.2 * G.3^-1)^3 ] Genus 46 action of group of order 720 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 46 action of group of order 648 via triangle group [ 2, 4, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 46 action of group of order 648 via triangle group [ 2, 4, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-4 * G.1 * G.2 * G.3^-4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-3 * G.2 * G.3^-1 ] Genus 46 action of group of order 540 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 46 action of group of order 540 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 46 action of group of order 432 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 432 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-4 * G.2, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 376 via triangle group [ 2, 4, 94 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-86 * G.1 * G.2 * G.3^-7 ] Genus 46 action of group of order 368 via triangle group [ 2, 4, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-84 * G.1 * G.2^-1 * G.3^-7 ] Genus 46 action of group of order 432 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 46 action of group of order 432 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2 ] Genus 46 action of group of order 432 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, (G.3 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^2 ] Genus 46 action of group of order 432 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, (G.3 * G.2^-1 * G.3)^3, G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 360 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.1 * G.3^8 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.3^-7 * G.1 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1)^6 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3 * G.2)^2 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3 * G.2^-2 * G.3^4 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^6 * G.2 * G.3^-6 * G.1 * G.3^2 * G.2^-1 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 46 action of group of order 324 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 46 action of group of order 288 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-3 * G.1 * G.3^7 * G.2^-1 * G.3^-5 ] Genus 46 action of group of order 288 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^28 * G.2 * G.3^-2 * G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3 ] Genus 46 action of group of order 288 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^29 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3^5 ] Genus 46 action of group of order 276 via triangle group [ 2, 6, 138 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-19 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 324 via triangle group [ 2, 9, 9 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.3^-1 * G.2)^3, G.2^-9 ] Genus 46 action of group of order 324 via triangle group [ 2, 9, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.2^-1 * G.3^2 * G.2^3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 46 action of group of order 250 via triangle group [ 2, 10, 25 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 46 action of group of order 250 via triangle group [ 2, 10, 25 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 46 action of group of order 250 via triangle group [ 2, 10, 25 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 ] Genus 46 action of group of order 250 via triangle group [ 2, 10, 25 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^3 * G.3^-3 ] Genus 46 action of group of order 250 via triangle group [ 2, 10, 25 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-3 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-13 ] Genus 46 action of group of order 230 via triangle group [ 2, 10, 115 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^3 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-14 * G.1 * G.3 ] Genus 46 action of group of order 224 via triangle group [ 2, 16, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^4 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 46 action of group of order 216 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, (G.2^-6 * G.3^2 * G.2^-1)^2 ] Genus 46 action of group of order 216 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.2^-1 * G.3^5 * G.2^-9 * G.3 * G.2^-2 ] Genus 46 action of group of order 216 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-3 * G.2, G.3^-1 * G.2^6 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 46 action of group of order 216 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 46 action of group of order 198 via triangle group [ 2, 33, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-6 * G.2^9 * G.3^-1 * G.2^2 * G.3^-13 * G.2 ] Genus 46 action of group of order 186 via triangle group [ 2, 93, 186 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^73 * G.2^-18 * G.3 ] Genus 46 action of group of order 188 via triangle group [ 2, 94, 94 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^20 * G.3^-74 ] Genus 46 action of group of order 184 via triangle group [ 2, 184, 184 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^19 * G.3^-73 ] Genus 46 action of group of order 1080 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 46 action of group of order 1080 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 46 action of group of order 1080 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 46 action of group of order 1080 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 46 action of group of order 324 via triangle group [ 3, 3, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 46 action of group of order 324 via triangle group [ 3, 3, 18 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 46 action of group of order 324 via triangle group [ 3, 3, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2 ] Genus 46 action of group of order 279 via triangle group [ 3, 3, 93 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 46 action of group of order 279 via triangle group [ 3, 3, 93 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^5 ] Genus 46 action of group of order 360 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 46 action of group of order 360 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 46 action of group of order 360 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 46 action of group of order 360 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-2)^2, G.3^6 ] Genus 46 action of group of order 240 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 46 action of group of order 240 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 46 action of group of order 216 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2^2 * G.1^-1 * G.3^3 ] Genus 46 action of group of order 216 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 46 action of group of order 216 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3 ] Genus 46 action of group of order 216 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 46 action of group of order 186 via triangle group [ 3, 6, 62 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 46 action of group of order 186 via triangle group [ 3, 6, 62 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.2^-2, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2^3 * G.1^-1 * G.3^3, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-3, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^8 ] Genus 46 action of group of order 216 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8 ] Genus 46 action of group of order 360 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 46 action of group of order 216 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 46 action of group of order 188 via triangle group [ 4, 4, 47 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^47 ] Genus 46 action of group of order 184 via triangle group [ 4, 4, 92 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^33 * G.2^-1 * G.3^-4 * G.1 * G.3^8 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.3^6, G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3 * G.1^-1, (G.1 * G.3 * G.2)^2, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, (G.2 * G.3^-2)^2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3 * G.1^-1, (G.1 * G.3^-1 * G.2)^2, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.3^-1 * G.2)^2, G.3^6 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, (G.3^-1 * G.1)^3 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-2 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 46 action of group of order 216 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, (G.3^-1 * G.1)^3, G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^9 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, (G.2 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, (G.3 * G.1 * G.4)^3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3, (G.2 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, (G.3 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.3 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.3 * G.1)^5 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.3 * G.1 * G.4)^3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 46 action of group of order 360 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 270 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4^2)^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.3 * G.1 * G.2 * G.1)^3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.3 * G.1)^3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, (G.2 * G.4^-2)^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, (G.2 * G.4^-2)^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4^2)^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 46 action of group of order 240 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-2 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1 * G.4)^3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1 * G.4)^3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 188 via quadrangle group [ 2, 2, 2, 47 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-23 * G.2 * G.1 * G.3 * G.4^-23 ] Genus 46 action of group of order 188 via quadrangle group [ 2, 2, 2, 47 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-40 * G.1^2 * G.4^-7 ] Genus 46 action of group of order 188 via quadrangle group [ 2, 2, 2, 47 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-30 * G.1 * G.2 * G.1 * G.2 * G.4^-15 ] Genus 46 action of group of order 184 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-23 * G.1 * G.4^-23 ] Genus 46 action of group of order 184 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-39 * G.2 * G.1^2 * G.4^-7 ] Genus 46 action of group of order 184 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-30 * G.1 * G.2 * G.4^-15 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.2 * G.4 * G.3)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, (G.2 * G.4^-1)^2, G.4^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.2 * G.4^-1 * G.2 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.2 * G.4 * G.3)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, (G.2^-1 * G.4 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.2^-1)^6 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 46 action of group of order 216 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^2 * G.2 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Largest orientation-preserving group for genus 46 has order 2160 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 46 has order 4320 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 46 has order 4320 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 46 has order 2160 ... group action with signature (0: +; [2,3,8]; {-}) Largest non-orientable group for non-orientable genus 47 has order 2160 ... group action with signature (0; +; [-]; {(2,3,8)}) Check total 437 : 254 chiral, 183 reflexible, with 36 non-orientable quotient actions Genus 47 actions: Genus 47 action of group of order 384 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-30 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 47 action of group of order 384 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-88 * G.1 * G.2 * G.3^-7 ] Genus 47 action of group of order 376 via triangle group [ 2, 4, 188 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-86 * G.1 * G.2^-1 * G.3^-7 ] Genus 47 action of group of order 282 via triangle group [ 2, 6, 141 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-19 * G.1 * G.3^9 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 47 action of group of order 288 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-3 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-8 ] Genus 47 action of group of order 288 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-4 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 47 action of group of order 256 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^20 * G.2 * G.3^-9 * G.1 * G.3^2 ] Genus 47 action of group of order 256 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^10 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^5 ] Genus 47 action of group of order 240 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 47 action of group of order 190 via triangle group [ 2, 95, 190 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^93 * G.3^-2 ] Genus 47 action of group of order 192 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^2 * G.2^-93 ] Genus 47 action of group of order 192 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-20 * G.2^11 * G.3^-2 * G.2^14 ] Genus 47 action of group of order 188 via triangle group [ 2, 188, 188 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^20 * G.3^-73 * G.2 ] Genus 47 action of group of order 336 via triangle group [ 3, 4, 7 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^48 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^12 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^12 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-11 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-1 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^12 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1^-1 ] Genus 47 action of group of order 192 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-17 * G.1 * G.3^2 * G.2 * G.3^-4 ] Genus 47 action of group of order 188 via triangle group [ 4, 4, 94 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^34 * G.2^-1 * G.3^-4 * G.1 * G.3^8 ] Genus 47 action of group of order 240 via triangle group [ 4, 5, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 368 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 47 action of group of order 276 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-48 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-41 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-32 * G.1^2 * G.4^-16 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-9 * G.1 * G.4^-1 * G.2 * G.4^13 * G.3 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^20 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^7 * G.2 * G.1 * G.4^14 * G.2 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-12 * G.1 * G.4^-1 * G.1 * G.4^-11 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 * G.1^2 * G.3 * G.1 * G.3 * G.4^-6 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.2 * G.4^-6 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^12 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^5 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-11 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.4^-6 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-10 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-9 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.4^3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-5 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-7 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^6 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^5 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 47 action of group of order 192 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 47 action of group of order 188 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-23 * G.2 * G.3 * G.4^-23 ] Genus 47 action of group of order 188 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-40 * G.1 * G.3 * G.4^-6 ] Genus 47 action of group of order 188 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-31 * G.1 * G.2 * G.4^-15 ] Largest orientation-preserving group for genus 47 has order 384 ... group action with signature (0: +; [2,4,96]; {-}) Largest group with or without reflections for genus 47 has order 768 ... group action with signature (0; +; [-]; {(2,4,96)}) Largest group with reflections for genus 47 has order 768 ... group action with signature (0; +; [-]; {(2,4,96)}) Largest chiral group for genus 47 has order 368 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 48 has order 368 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 229 : 148 chiral, 81 reflexible, with 30 non-orientable quotient actions Genus 48 actions: Genus 48 action of group of order 408 via triangle group [ 2, 4, 51 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-35 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 48 action of group of order 392 via triangle group [ 2, 4, 98 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-98 ] Genus 48 action of group of order 384 via triangle group [ 2, 4, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-88 * G.1 * G.2^-1 * G.3^-7 ] Genus 48 action of group of order 300 via triangle group [ 2, 6, 50 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^38 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^5 ] Genus 48 action of group of order 272 via triangle group [ 2, 8, 34 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-12 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-14 ] Genus 48 action of group of order 260 via triangle group [ 2, 10, 26 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^4 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3^15 ] Genus 48 action of group of order 240 via triangle group [ 2, 10, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.1 * G.3^7 * G.2 * G.3^-16 ] Genus 48 action of group of order 240 via triangle group [ 2, 12, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-5 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 48 action of group of order 252 via triangle group [ 2, 14, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-6 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3^9 * G.2^-1 * G.3^-6 ] Genus 48 action of group of order 224 via triangle group [ 2, 14, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-3 * G.3^4)^2, G.3^9 * G.2 * G.1 * G.3^6 ] Genus 48 action of group of order 208 via triangle group [ 2, 26, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-14 * G.3^2 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 48 action of group of order 204 via triangle group [ 2, 34, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-5 * G.2^11 * G.3^-2 * G.2^12 * G.3^-3 ] Genus 48 action of group of order 200 via triangle group [ 2, 50, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-22 * G.2^11 * G.3^-1 * G.2^14 * G.3^-1 ] Genus 48 action of group of order 204 via triangle group [ 2, 51, 51 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-37 * G.2^11 * G.3^-1 ] Genus 48 action of group of order 194 via triangle group [ 2, 97, 194 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^94 * G.3^-2 * G.2 ] Genus 48 action of group of order 196 via triangle group [ 2, 98, 98 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^3 * G.2^-93 * G.3 ] Genus 48 action of group of order 192 via triangle group [ 2, 192, 192 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^2 * G.2^-92 * G.3 ] Genus 48 action of group of order 291 via triangle group [ 3, 3, 97 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 48 action of group of order 291 via triangle group [ 3, 3, 97 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1 * G.3^4 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 48 action of group of order 196 via triangle group [ 4, 4, 49 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-49 ] Genus 48 action of group of order 192 via triangle group [ 4, 4, 96 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^35 * G.2^-1 * G.3^-4 * G.1 * G.3^8 ] Genus 48 action of group of order 196 via quadrangle group [ 2, 2, 2, 49 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-24 * G.2 * G.1 * G.3 * G.4^-24 ] Genus 48 action of group of order 196 via quadrangle group [ 2, 2, 2, 49 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-42 * G.1^2 * G.4^-7 ] Genus 48 action of group of order 196 via quadrangle group [ 2, 2, 2, 49 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^49 ] Genus 48 action of group of order 192 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-24 * G.1 * G.4^-24 ] Genus 48 action of group of order 192 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-41 * G.2 * G.1^2 * G.4^-7 ] Genus 48 action of group of order 192 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-32 * G.1 * G.2 * G.4^-15 ] Largest orientation-preserving group for genus 48 has order 408 ... group action with signature (0: +; [2,4,51]; {-}) Largest group with or without reflections for genus 48 has order 816 ... group action with signature (0; +; [-]; {(2,4,51)}) Largest group with reflections for genus 48 has order 816 ... group action with signature (0; +; [-]; {(2,4,51)}) No chiral group action for genus 48 Largest non-orientable group for non-orientable genus 49 has order 408 ... group action with signature (0; +; [-]; {(2,4,51)}) Check total 27 : 0 chiral, 27 reflexible, with 9 non-orientable quotient actions Genus 49 actions: Genus 49 action of group of order 1440 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 1152 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 49 action of group of order 1008 via triangle group [ 2, 3, 14 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 1008 via triangle group [ 2, 3, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^5 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 1920 via triangle group [ 2, 4, 5 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 1920 via triangle group [ 2, 4, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 1920 via triangle group [ 2, 4, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 1152 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 49 action of group of order 1152 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^6 ] Genus 49 action of group of order 1152 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 896 via triangle group [ 2, 4, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4 ] Genus 49 action of group of order 640 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, G.3^10, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 49 action of group of order 640 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^10, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 49 action of group of order 640 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^10, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 ] Genus 49 action of group of order 576 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^12 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-7 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^6 * G.2 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-9 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-5 ] Genus 49 action of group of order 512 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 49 action of group of order 480 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-4)^2, G.3^-2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 480 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 448 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-14 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 49 action of group of order 416 via triangle group [ 2, 4, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-37 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 49 action of group of order 400 via triangle group [ 2, 4, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-100 ] Genus 49 action of group of order 392 via triangle group [ 2, 4, 196 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-8 * G.1 * G.2^-1 * G.3^-89 ] Genus 49 action of group of order 960 via triangle group [ 2, 5, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.2 * G.3^-2 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 960 via triangle group [ 2, 5, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 960 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6 ] Genus 49 action of group of order 720 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3^2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-2 * G.1 * G.3^2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, (G.2 * G.3^-1 * G.2)^4 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 576 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.2^-2 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3^2 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, (G.2 * G.3^-1 * G.2)^4 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, (G.2 * G.3^-1 * G.2)^4 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-3 * G.2 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-4, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-3 * G.3^-3 * G.2^2 ] Genus 49 action of group of order 384 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2^-3 * G.3^-3 * G.2^2 ] Genus 49 action of group of order 360 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-8 * G.1 * G.2 * G.3^-6 ] Genus 49 action of group of order 360 via triangle group [ 2, 6, 15 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 49 action of group of order 360 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 360 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2^-2 * G.3)^3 ] Genus 49 action of group of order 360 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2^-2 * G.3)^3 ] Genus 49 action of group of order 312 via triangle group [ 2, 6, 39 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-2 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 49 action of group of order 306 via triangle group [ 2, 6, 51 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^40 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 49 action of group of order 294 via triangle group [ 2, 6, 147 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-21 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 ] Genus 49 action of group of order 448 via triangle group [ 2, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 49 action of group of order 336 via triangle group [ 2, 7, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3 * G.2^-1 * G.3)^3 ] Genus 49 action of group of order 288 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 288 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2^-1 * G.3)^6 ] Genus 49 action of group of order 288 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 320 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.2^10 ] Genus 49 action of group of order 320 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.3, G.2^10, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 49 action of group of order 320 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.3^-3, G.2^10, (G.2 * G.3^-1 * G.2^3)^2 ] Genus 49 action of group of order 320 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-3 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^10 ] Genus 49 action of group of order 320 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.3^3, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12, G.2^2 * G.3^-1 * G.2^4 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.3^2 * G.2^3 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.3^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.2^12 ] Genus 49 action of group of order 288 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.3^-12 ] Genus 49 action of group of order 240 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^-1 * G.1 * G.3^8 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^5 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.2^-4 * G.3^3 * G.2^-1)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.2^3 * G.3^-1 * G.2 * G.3^-1 * G.2^2)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-2 * G.3 * G.2^-2 * G.3^2 * G.2^-6 * G.3 * G.2^-2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-4 * G.3 * G.2^8 * G.1 * G.2^-3, G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-6 * G.3 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2^-3 * G.3^3 * G.2^-2)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2^-3 * G.3^-1 * G.1 * G.3^3 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.1 * G.3^7 * G.2^-1 * G.3^-6 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^2 * G.3^-1 * G.2^2 * G.3^-3, G.2^-4 * G.3 * G.2^8 * G.1 * G.2^-3 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-7 * G.3^-1 * G.1 * G.3^2 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-1 * G.1 * G.3^8 * G.2 * G.3^-6 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4, G.2^-4 * G.3 * G.2^8 * G.1 * G.2^-3 ] Genus 49 action of group of order 256 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.1 * G.3^9 * G.2^-1 * G.3^-6, G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-6 * G.3^-1 * G.2 ] Genus 49 action of group of order 224 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^10 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 224 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.3^-5, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1 ] Genus 49 action of group of order 240 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, (G.2 * G.3^-2 * G.2)^2 ] Genus 49 action of group of order 240 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-4 * G.3^-4, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 49 action of group of order 216 via triangle group [ 2, 27, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-27 ] Genus 49 action of group of order 224 via triangle group [ 2, 28, 28 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^10 * G.2^-15 ] Genus 49 action of group of order 224 via triangle group [ 2, 28, 28 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-10 * G.3^2 * G.2^-1 * G.3 ] Genus 49 action of group of order 224 via triangle group [ 2, 28, 28 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^-3 * G.3^8 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-10 * G.3^2 ] Genus 49 action of group of order 224 via triangle group [ 2, 28, 28 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-10 * G.3 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 224 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-11 * G.3^3 * G.2^-10 * G.3^2 ] Genus 49 action of group of order 210 via triangle group [ 2, 30, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^2 * G.2^-4 * G.3^5 ] Genus 49 action of group of order 216 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-8 * G.2^9 * G.3^-2 * G.2^16 ] Genus 49 action of group of order 216 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-8 * G.2^11 * G.3^-4 * G.2 * G.3^-12 ] Genus 49 action of group of order 208 via triangle group [ 2, 52, 52 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-24 * G.2^11 * G.3^-2 * G.2^12 * G.3^-2 ] Genus 49 action of group of order 198 via triangle group [ 2, 99, 198 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^95 * G.3^-4 ] Genus 49 action of group of order 200 via triangle group [ 2, 100, 100 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^4 * G.2^-95 ] Genus 49 action of group of order 196 via triangle group [ 2, 196, 196 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^3 * G.2^-94 ] Genus 49 action of group of order 720 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 49 action of group of order 576 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, (G.1 * G.3 * G.2)^4 ] Genus 49 action of group of order 576 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 49 action of group of order 576 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 49 action of group of order 504 via triangle group [ 3, 3, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 ] Genus 49 action of group of order 504 via triangle group [ 3, 3, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 576 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1)^4, (G.2 * G.1^-1 * G.3)^3 ] Genus 49 action of group of order 576 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 49 action of group of order 576 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 49 action of group of order 384 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 49 action of group of order 288 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 49 action of group of order 360 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3 ] Genus 49 action of group of order 240 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, (G.1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 49 action of group of order 240 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, (G.1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.3^6 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1^-1 * G.2^-1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.3^6 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 49 action of group of order 240 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 320 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 288 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6 ] Genus 49 action of group of order 288 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6 ] Genus 49 action of group of order 288 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1^-1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1^-1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3 * G.2^-1)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.2 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, (G.1 * G.3^-3)^2, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-2 * G.3^3 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^8 ] Genus 49 action of group of order 256 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8, G.3^-3 * G.2 * G.1^2 * G.3^3 * G.2 ] Genus 49 action of group of order 240 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1 * G.3^2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 49 action of group of order 240 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 49 action of group of order 240 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, (G.1 * G.3 * G.2)^2 ] Genus 49 action of group of order 240 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-2)^2, (G.2 * G.3^-2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 49 action of group of order 224 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-4 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 49 action of group of order 208 via triangle group [ 4, 4, 26 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^16 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-7 * G.1^-1 ] Genus 49 action of group of order 208 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^4 ] Genus 49 action of group of order 208 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 49 action of group of order 200 via triangle group [ 4, 4, 50 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 49 action of group of order 200 via triangle group [ 4, 4, 50 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^36 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 49 action of group of order 200 via triangle group [ 4, 4, 50 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 49 action of group of order 196 via triangle group [ 4, 4, 98 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-42 * G.1 * G.2^-1 * G.3^-6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-1)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-1)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^6 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^8 ] Genus 49 action of group of order 576 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^12 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.3 * G.1)^8 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^12 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^24 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^24 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^24 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.2 * G.4^-1)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 384 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.3 * G.1)^5, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.2 * G.1)^5, G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-5, (G.1 * G.2)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-5, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5, (G.1 * G.2)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-5, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 320 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^24 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^8 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^12 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^12 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^12 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.2 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, (G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, (G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^4 * G.1^2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^8 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 49 action of group of order 256 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, (G.1 * G.3)^6 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, (G.1 * G.3)^6 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, (G.1 * G.3)^6 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, (G.1 * G.3)^6 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10, G.1 * G.3 * G.4^-4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^-3 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^10, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^-3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^10, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.4^10, G.1 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^10, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^10, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^10, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.1 * G.4^-2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^10, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^3 * G.2 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^5, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^10, G.3 * G.2 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^10, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 240 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-14 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-6 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.4^-7 * G.2 * G.1^2 * G.3 * G.2 * G.4^4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-8 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^7 * G.3 * G.4^-1 * G.2 * G.4^-4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-8 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 224 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.4^4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^4 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-18 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-6 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12 * G.1^2 * G.4^6 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-10 * G.2 * G.4 * G.1 * G.4^5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^6 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-18 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^6 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.2 * G.4^-2 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^6 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-7 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^7 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-18 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-11 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^3 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^7 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-4 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4^3 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-10 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 49 action of group of order 216 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-10 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^6 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.1 * G.4^4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-9 * G.2 * G.4^-4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^9 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 * G.3 * G.1 * G.4^5 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-26 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-8 * G.2 * G.4^7 * G.3 * G.2 * G.4^5 * G.3 * G.4^-4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^6 * G.3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-8 * G.1 * G.4^4 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^7 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^8 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8 * G.2 * G.4^-8 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^7 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4^2 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-13 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-21 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 49 action of group of order 208 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^13 * G.2 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-9 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^4 * G.3 * G.4^-7 * G.2 * G.1 * G.3 * G.2 * G.4^4 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^8 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-7 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-8 * G.2 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-5 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^12 * G.3 * G.1 * G.4 * G.1^2 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 * G.3 * G.1 * G.4^4 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.4^3 * G.3 * G.4^6 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 49 action of group of order 204 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-11 * G.2 * G.4^13 * G.3 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-9 * G.1 * G.4^-1 * G.2 * G.4^11 * G.3 * G.4^-1 * G.2 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-19 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.4^-3 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-19 * G.1 * G.4 * G.1^2 * G.3 * G.4^-4 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-4 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^12 * G.2 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-8 * G.1^2 * G.4^-1 * G.1 * G.4^14 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-50 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-43 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 49 action of group of order 200 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^34 * G.2 * G.1 * G.2 * G.1 * G.4^14 ] Genus 49 action of group of order 196 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-24 * G.2 * G.3 * G.4^-24 ] Genus 49 action of group of order 196 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-42 * G.1 * G.3 * G.4^-6 ] Genus 49 action of group of order 196 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^34 * G.2 * G.1 * G.4^14 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, (G.3^-1 * G.1)^12, G.2 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, (G.3^-1 * G.1)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.3^-1 * G.1 * G.3 * G.1)^3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.3^-1 * G.1 * G.3 * G.1)^3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.1 * G.2)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1, G.4^-1)^2, (G.2^-1 * G.4^-1)^6, G.3 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, (G.2^-1, G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1, G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, (G.2^-1, G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.2^-1, G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, (G.2^-1, G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.1^2 * G.2 * G.4 * G.2^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.4 * G.1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.3)^4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1, (G.3 * G.1)^3, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.3 * G.2^-1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, (G.2^-1 * G.3)^4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 49 action of group of order 288 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3)^4 ] Largest orientation-preserving group for genus 49 has order 1920 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 49 has order 3840 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 49 has order 3840 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 49 has order 1920 ... group action with signature (0: +; [2,4,5]; {-}) Largest non-orientable group for non-orientable genus 50 has order 1920 ... group action with signature (0; +; [-]; {(2,4,5)}) Check total 2874 : 1378 chiral, 1496 reflexible, with 299 non-orientable quotient actions Genus 50 actions: Genus 50 action of group of order 1092 via triangle group [ 2, 3, 13 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 50 action of group of order 1176 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 50 action of group of order 1176 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 50 action of group of order 408 via triangle group [ 2, 4, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-102 ] Genus 50 action of group of order 400 via triangle group [ 2, 4, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-9 * G.1 * G.2^-1 * G.3^-90 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 50 action of group of order 588 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1 ] Genus 50 action of group of order 336 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 50 action of group of order 336 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 50 action of group of order 336 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 50 action of group of order 336 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 50 action of group of order 312 via triangle group [ 2, 6, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-30 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-15 ] Genus 50 action of group of order 300 via triangle group [ 2, 6, 150 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-20 * G.1 * G.3 * G.2 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 50 action of group of order 392 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 50 action of group of order 392 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 272 via triangle group [ 2, 8, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-12 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-16 ] Genus 50 action of group of order 264 via triangle group [ 2, 12, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 50 action of group of order 240 via triangle group [ 2, 12, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 240 via triangle group [ 2, 15, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 50 action of group of order 252 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 50 action of group of order 252 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2^2 * G.3^-1 * G.2^10 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 50 action of group of order 252 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^9 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-3 ] Genus 50 action of group of order 252 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-3 ] Genus 50 action of group of order 240 via triangle group [ 2, 20, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 50 action of group of order 220 via triangle group [ 2, 22, 110 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-10 * G.3^2 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 50 action of group of order 210 via triangle group [ 2, 42, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-9 * G.3^2 * G.2^-6 * G.3^3 * G.2^-1 ] Genus 50 action of group of order 208 via triangle group [ 2, 52, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-14 * G.3^2 * G.2^-8 * G.3^2 ] Genus 50 action of group of order 202 via triangle group [ 2, 101, 202 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^96 * G.3^-4 * G.2 ] Genus 50 action of group of order 204 via triangle group [ 2, 102, 102 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^5 * G.2^-95 * G.3 ] Genus 50 action of group of order 200 via triangle group [ 2, 200, 200 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^4 * G.2^-94 * G.3 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 50 action of group of order 1176 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 50 action of group of order 312 via triangle group [ 3, 3, 52 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 50 action of group of order 312 via triangle group [ 3, 3, 52 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 50 action of group of order 588 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 50 action of group of order 294 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.3 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-2 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2, G.1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 50 action of group of order 392 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 50 action of group of order 204 via triangle group [ 4, 4, 51 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^37 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 50 action of group of order 204 via triangle group [ 4, 4, 51 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1 * G.3^-2 ] Genus 50 action of group of order 204 via triangle group [ 4, 4, 51 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-2 ] Genus 50 action of group of order 200 via triangle group [ 4, 4, 100 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^36 * G.2^-1 * G.1 * G.3^13 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 588 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 * G.4^-1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^2 * G.2 * G.4^2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-2 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^2 * G.2 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 392 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.3 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-8 * G.2 * G.3 * G.1 * G.4^-8 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-6 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-3 * G.3 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^8 * G.2 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-25 * G.2 * G.1 * G.3 * G.4^-25 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-44 * G.1^2 * G.4^-7 ] Genus 50 action of group of order 204 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^51 ] Genus 50 action of group of order 200 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-25 * G.1 * G.4^-25 ] Genus 50 action of group of order 200 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-43 * G.2 * G.1^2 * G.4^-7 ] Genus 50 action of group of order 200 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^34 * G.2 * G.1 * G.4^15 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3^-1 * G.1 * G.3 * G.1)^7, G.2 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.3^-2 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^7 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.4 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^14, G.2 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, (G.2 * G.1)^7 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.3 * G.1)^7 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.4^-1 * G.2^-1)^7, G.3 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.2^-1 * G.3 * G.2^-1 * G.4)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.2^-1 * G.3 * G.2^-1 * G.4)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^7 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^7, G.3 * G.1^-1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 50 action of group of order 294 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 ] Largest orientation-preserving group for genus 50 has order 1176 ... group action with signature (0: +; [3,3,4]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 50 has order 2184 ... group action with signature (0; +; [-]; {(2,3,13)}) Largest group with reflections for genus 50 has order 2184 ... group action with signature (0; +; [-]; {(2,3,13)}) Largest chiral group for genus 50 has order 1176 ... group action with signature (0: +; [3,3,4]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest non-orientable group for non-orientable genus 51 has order 1092 ... group action with signature (0; +; [-]; {(2,3,13)}) Check total 526 : 424 chiral, 102 reflexible, with 17 non-orientable quotient actions Genus 51 actions: Genus 51 action of group of order 1200 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12, G.3^-3 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 1200 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 1200 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12, G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^2 * G.3^-3 * G.1 * G.3^2 ] Genus 51 action of group of order 750 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^6 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3^-4 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^3 * G.2^-1 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 51 action of group of order 800 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 51 action of group of order 600 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 600 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-3 * G.1 * G.3 ] Genus 51 action of group of order 600 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 51 action of group of order 600 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 600 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 51 action of group of order 500 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.3^-1 * G.2)^5 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.1 * G.3^2 * G.2 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-9 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-6 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-9 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 480 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.2 ] Genus 51 action of group of order 440 via triangle group [ 2, 4, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3^8 * G.2 * G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 440 via triangle group [ 2, 4, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-5 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-8 ] Genus 51 action of group of order 432 via triangle group [ 2, 4, 54 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-38 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 51 action of group of order 416 via triangle group [ 2, 4, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-37 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 51 action of group of order 416 via triangle group [ 2, 4, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-104 ] Genus 51 action of group of order 408 via triangle group [ 2, 4, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-10 * G.1 * G.2^-1 * G.3^-91 ] Genus 51 action of group of order 480 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 480 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 51 action of group of order 336 via triangle group [ 2, 6, 28 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.3^3 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.3^-1 * G.1 * G.2^-3 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.3^2 * G.2^-4 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 51 action of group of order 320 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 51 action of group of order 320 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 51 action of group of order 320 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 51 action of group of order 320 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 51 action of group of order 288 via triangle group [ 2, 8, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^7 * G.2 * G.1 * G.3^2 * G.2 * G.3^-6 * G.1 * G.3 ] Genus 51 action of group of order 288 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-4 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 51 action of group of order 288 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^17 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 ] Genus 51 action of group of order 288 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^16 * G.2 * G.3^-2 * G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3 ] Genus 51 action of group of order 272 via triangle group [ 2, 8, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-8 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 272 via triangle group [ 2, 8, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-7 * G.1 * G.3^8 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-9 * G.1 * G.3^2 * G.2^-1 ] Genus 51 action of group of order 300 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3 * G.2^-4 * G.3^-1 * G.1 * G.3^2 ] Genus 51 action of group of order 300 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-3 * G.3^4 ] Genus 51 action of group of order 300 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 300 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 300 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 51 action of group of order 238 via triangle group [ 2, 14, 119 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^3 * G.2^-5 * G.3^3, G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-10 ] Genus 51 action of group of order 240 via triangle group [ 2, 15, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^11 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 2, 20, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^6 * G.2^-1 * G.3^3 * G.2^-8 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 240 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-6 * G.3 * G.2^-3 * G.3^2 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 ] Genus 51 action of group of order 240 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^6 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 240 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 224 via triangle group [ 2, 28, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3^10 * G.2^-1 * G.3^4 * G.2^-10 * G.3^2 ] Genus 51 action of group of order 224 via triangle group [ 2, 28, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-15 * G.3^4 * G.2^-5 * G.3^4 ] Genus 51 action of group of order 220 via triangle group [ 2, 44, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^3 * G.2^-8 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 51 action of group of order 220 via triangle group [ 2, 44, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3 * G.2^-2 * G.3^2 * G.2^-3 * G.3^2 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 ] Genus 51 action of group of order 216 via triangle group [ 2, 54, 54 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-40 * G.2^11 * G.3^-1 ] Genus 51 action of group of order 210 via triangle group [ 2, 70, 105 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-6 * G.2^11 * G.3^-2 * G.2^14 * G.3^-1 ] Genus 51 action of group of order 206 via triangle group [ 2, 103, 206 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^97 * G.3^-6 ] Genus 51 action of group of order 208 via triangle group [ 2, 104, 104 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^6 * G.2^-97 ] Genus 51 action of group of order 208 via triangle group [ 2, 104, 104 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-24 * G.2^11 * G.3^-2 * G.2^14 ] Genus 51 action of group of order 204 via triangle group [ 2, 204, 204 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^5 * G.2^-96 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.1^-1 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 ] Genus 51 action of group of order 600 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 51 action of group of order 375 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 51 action of group of order 336 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-4 * G.1^2 * G.3^5 ] Genus 51 action of group of order 336 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-6 * G.1^2 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 309 via triangle group [ 3, 3, 103 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2 * G.1 * G.3^4 * G.2 * G.1 ] Genus 51 action of group of order 309 via triangle group [ 3, 3, 103 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-4 ] Genus 51 action of group of order 300 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 300 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 300 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2 ] Genus 51 action of group of order 240 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, (G.2 * G.3^-1)^4 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1, (G.1 * G.3^-1)^4 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3^2 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 51 action of group of order 400 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1 * G.3^-2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.1 * G.2^-1 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 51 action of group of order 300 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.3 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^5 * G.2 * G.1 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 51 action of group of order 220 via triangle group [ 4, 4, 22 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 51 action of group of order 220 via triangle group [ 4, 4, 22 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1^-1 * G.3^5 ] Genus 51 action of group of order 216 via triangle group [ 4, 4, 27 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^19 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^16 * G.2 * G.1 * G.3 * G.2 * G.3^-7 * G.1 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^16 * G.2 * G.1 * G.3 * G.2 * G.3^-7 * G.1^-1 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^38 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^16 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-7 * G.1 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 208 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.1^-1 * G.3^3 ] Genus 51 action of group of order 204 via triangle group [ 4, 4, 102 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^37 * G.2^-1 * G.1 * G.3^13 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-2)^2, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-2)^2, G.3^6 ] Genus 51 action of group of order 240 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^10 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 51 action of group of order 400 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.3 * G.4^-3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 51 action of group of order 300 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 250 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.1)^5, (G.3 * G.1)^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.1 * G.4^6 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.2 * G.4^-4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.4^3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.4 * G.2 * G.4^-3 * G.1 * G.4)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.3 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 * G.2 * G.3 * G.1, G.4^-12 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^6 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.2 * G.4^-4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-12, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, (G.4 * G.2 * G.4^-3 * G.1 * G.4)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^7 * G.1^2 * G.4^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^7 * G.1^2 * G.4^5, G.3 * G.4^-2 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-12, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.4^3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-7 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-2 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-5 * G.1 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 51 action of group of order 220 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6 * G.1^2 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-16 * G.2 * G.4^7 * G.3 * G.4^-3 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^16 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-13 * G.2 * G.1 * G.3 * G.4^-13 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^20 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^14 * G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-15 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-20 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^16 * G.2 * G.4^-7 * G.1 * G.4^3 ] Genus 51 action of group of order 216 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^15 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-52 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-52 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^36 * G.2 * G.1 * G.2 * G.1 * G.4^14 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.4 * G.3 * G.4^-13 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^19 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^13 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-13 * G.1 * G.4^-1 * G.1 * G.4^-12 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-5 * G.2 * G.4^9 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^6 * G.3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 * G.1 * G.4^7 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-18 * G.1 * G.2 * G.1 * G.4^6 * G.2 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^7 * G.3 * G.4^-5 * G.2 * G.1 * G.4^13 ] Genus 51 action of group of order 208 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^18 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4^2 ] Genus 51 action of group of order 204 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-25 * G.2 * G.3 * G.4^-25 ] Genus 51 action of group of order 204 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-44 * G.1 * G.3 * G.4^-6 ] Genus 51 action of group of order 204 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^36 * G.2 * G.1 * G.4^14 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.2 * G.1)^5 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3^-1)^4, G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, G.3^-1 * G.4^-2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.3 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.1 * G.3^-1 * G.4 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.2 * G.4 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.3 * G.1)^3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, (G.2^-1 * G.4^-1)^4, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2^-1 * G.3 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.4 * G.3)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.1 * G.4 * G.3)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2^-1 * G.1)^4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3)^2 ] Genus 51 action of group of order 240 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Largest orientation-preserving group for genus 51 has order 1200 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 51 has order 2400 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 51 has order 2400 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 51 has order 1200 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 52 has order 480 ... group action with signature (0; +; [-]; {(2,6,8)}) Check total 661 : 456 chiral, 205 reflexible, with 74 non-orientable quotient actions Genus 52 actions: Genus 52 action of group of order 2448 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 52 action of group of order 2448 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 52 action of group of order 424 via triangle group [ 2, 4, 106 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-106 ] Genus 52 action of group of order 416 via triangle group [ 2, 4, 208 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-11 * G.1 * G.2^-1 * G.3^-92 ] Genus 52 action of group of order 360 via triangle group [ 2, 6, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-5 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 52 action of group of order 324 via triangle group [ 2, 6, 54 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-36 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-10 ] Genus 52 action of group of order 324 via triangle group [ 2, 6, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-25 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 52 action of group of order 324 via triangle group [ 2, 6, 54 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3^2 * G.2^-1 ] Genus 52 action of group of order 324 via triangle group [ 2, 6, 54 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 52 action of group of order 312 via triangle group [ 2, 6, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^23 * G.2 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 52 action of group of order 280 via triangle group [ 2, 10, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-6 ] Genus 52 action of group of order 260 via triangle group [ 2, 10, 130 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^8 * G.2 * G.1 * G.2 * G.3^-16 * G.1 ] Genus 52 action of group of order 288 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.2^2 * G.3^-2 * G.2 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-1 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.2^3 * G.3^-1 * G.2^2 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^3 * G.3^-2 * G.2 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-3 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-2 * G.2 ] Genus 52 action of group of order 272 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-2 * G.2^2 * G.3^-3 ] Genus 52 action of group of order 234 via triangle group [ 2, 18, 117 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-10 ] Genus 52 action of group of order 240 via triangle group [ 2, 24, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 52 action of group of order 224 via triangle group [ 2, 28, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^4 * G.2^-2 * G.3^4 * G.2^-1 ] Genus 52 action of group of order 216 via triangle group [ 2, 54, 108 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-26 * G.2^11 * G.3^-2 * G.2^15 ] Genus 52 action of group of order 210 via triangle group [ 2, 105, 210 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^98 * G.3^-6 * G.2 ] Genus 52 action of group of order 212 via triangle group [ 2, 106, 106 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^7 * G.2^-97 * G.3 ] Genus 52 action of group of order 208 via triangle group [ 2, 208, 208 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^6 * G.2^-96 * G.3 ] Genus 52 action of group of order 212 via triangle group [ 4, 4, 53 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.1^-1 * G.3 * G.2^-1 * G.3^4 ] Genus 52 action of group of order 212 via triangle group [ 4, 4, 53 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 52 action of group of order 212 via triangle group [ 4, 4, 53 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^39 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 52 action of group of order 208 via triangle group [ 4, 4, 104 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^38 * G.2^-1 * G.1 * G.3^13 ] Genus 52 action of group of order 240 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-5, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 52 action of group of order 216 via triangle group [ 4, 6, 9 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^9 ] Genus 52 action of group of order 216 via triangle group [ 4, 6, 9 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 52 action of group of order 216 via triangle group [ 4, 6, 9 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2^2 * G.3^-1 * G.1, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 52 action of group of order 408 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 52 action of group of order 212 via quadrangle group [ 2, 2, 2, 53 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-26 * G.2 * G.1 * G.3 * G.4^-26 ] Genus 52 action of group of order 212 via quadrangle group [ 2, 2, 2, 53 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-46 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 52 action of group of order 212 via quadrangle group [ 2, 2, 2, 53 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-37 * G.1^2 * G.4^-16 ] Genus 52 action of group of order 208 via quadrangle group [ 2, 2, 2, 104 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-26 * G.1 * G.4^-26 ] Genus 52 action of group of order 208 via quadrangle group [ 2, 2, 2, 104 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-45 * G.1 * G.3 * G.4^-6 ] Genus 52 action of group of order 208 via quadrangle group [ 2, 2, 2, 104 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^36 * G.2 * G.1 * G.4^15 ] Largest orientation-preserving group for genus 52 has order 2448 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 52 has order 4896 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 52 has order 4896 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 52 has order 408 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 53 has order 408 ... group action with signature (0; +; [2]; {(2,4)}) Check total 114 : 76 chiral, 38 reflexible, with 10 non-orientable quotient actions Genus 53 actions: Genus 53 action of group of order 832 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 53 action of group of order 832 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 53 action of group of order 832 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 53 action of group of order 832 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 53 action of group of order 624 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 53 action of group of order 624 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 53 action of group of order 520 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 53 action of group of order 520 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 53 action of group of order 480 via triangle group [ 2, 4, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-14 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 448 via triangle group [ 2, 4, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-41 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 448 via triangle group [ 2, 4, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-14 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 432 via triangle group [ 2, 4, 108 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-108 ] Genus 53 action of group of order 424 via triangle group [ 2, 4, 212 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-12 * G.1 * G.2^-1 * G.3^-93 ] Genus 53 action of group of order 624 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 624 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 53 action of group of order 624 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.1 ] Genus 53 action of group of order 624 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 390 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.1 ] Genus 53 action of group of order 390 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 ] Genus 53 action of group of order 384 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^4 * G.2^2 * G.1 * G.3^3, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 53 action of group of order 384 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-7 ] Genus 53 action of group of order 384 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 53 action of group of order 336 via triangle group [ 2, 6, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 53 action of group of order 318 via triangle group [ 2, 6, 159 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^41 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 53 action of group of order 416 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 53 action of group of order 416 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 53 action of group of order 416 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 53 action of group of order 416 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 320 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 53 action of group of order 320 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^10 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 288 via triangle group [ 2, 8, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^17 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.3^6 ] Genus 53 action of group of order 288 via triangle group [ 2, 8, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^17 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2 * G.3^-7 * G.1 * G.3^3 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 * G.2, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2^-3 * G.3^-4, G.2^12 ] Genus 53 action of group of order 312 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2^12 ] Genus 53 action of group of order 264 via triangle group [ 2, 12, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-4 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 53 action of group of order 256 via triangle group [ 2, 16, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3^7 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 53 action of group of order 260 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 53 action of group of order 260 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 53 action of group of order 240 via triangle group [ 2, 20, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-8 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 53 action of group of order 240 via triangle group [ 2, 24, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-1 * G.3 * G.2^10 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 53 action of group of order 240 via triangle group [ 2, 24, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-1 * G.3 * G.2^10 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 240 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-30 ] Genus 53 action of group of order 224 via triangle group [ 2, 56, 56 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-27 * G.2^28 * G.3^-1 ] Genus 53 action of group of order 224 via triangle group [ 2, 56, 56 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-11 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 53 action of group of order 214 via triangle group [ 2, 107, 214 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^99 * G.3^-8 ] Genus 53 action of group of order 216 via triangle group [ 2, 108, 108 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^8 * G.2^-99 ] Genus 53 action of group of order 212 via triangle group [ 2, 212, 212 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^7 * G.2^-98 ] Genus 53 action of group of order 312 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 53 action of group of order 312 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 53 action of group of order 312 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1 * G.2^3 * G.3^-1 * G.2 * G.3^-1 ] Genus 53 action of group of order 312 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 53 action of group of order 416 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 53 action of group of order 312 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 53 action of group of order 312 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 53 action of group of order 260 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 53 action of group of order 260 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 53 action of group of order 240 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 53 action of group of order 224 via triangle group [ 4, 4, 28 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^22 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 53 action of group of order 224 via triangle group [ 4, 4, 28 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-5 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^2 * G.2 ] Genus 53 action of group of order 224 via triangle group [ 4, 4, 28 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^21 * G.2^-1 * G.3^-2 * G.1 * G.3^4 ] Genus 53 action of group of order 224 via triangle group [ 4, 4, 28 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-21 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 53 action of group of order 216 via triangle group [ 4, 4, 54 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-46 * G.1 * G.2 * G.3^-7 ] Genus 53 action of group of order 212 via triangle group [ 4, 4, 106 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^39 * G.2^-1 * G.1 * G.3^13 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^26 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^26 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 53 action of group of order 416 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 53 action of group of order 260 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-3, (G.1 * G.2)^4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3, (G.1 * G.2)^4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, (G.1 * G.2)^6 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^6 * G.3 * G.4^-2 * G.1 * G.2 * G.4^6 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^10 * G.1^2 * G.4^5 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.3 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4^5 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 53 action of group of order 240 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-28 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-10 * G.2 * G.4^7 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 * G.2 * G.4^5 * G.3 * G.4^-8 * G.1 * G.4^4 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8 * G.2 * G.4^-8 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^9 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^9 * G.3 * G.4^-3 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^10 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-18 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^3 * G.1 * G.4 * G.1^2 * G.4^6 * G.3 * G.4^-2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.2 * G.4^6 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-8 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-3 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^6 * G.3 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-5 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^6 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 * G.2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-6 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-6 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^3 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.2 * G.4^6 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-11 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^9 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^23 * G.1^2 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-11 * G.1 * G.2 * G.4^-1 * G.1 * G.4^14 * G.2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^9 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.4^3 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^4 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.4^-9 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 224 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^9 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.4^3 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^9 * G.3 * G.4^-1 * G.2 * G.4^16 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^8 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^14 * G.3 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^21 * G.3 * G.1 * G.4^5 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-22 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^13 * G.2 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^14 * G.2 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-54 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-54 ] Genus 53 action of group of order 216 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-38 * G.1^2 * G.4^-16 ] Genus 53 action of group of order 212 via quadrangle group [ 2, 2, 2, 106 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-26 * G.2 * G.3 * G.4^-26 ] Genus 53 action of group of order 212 via quadrangle group [ 2, 2, 2, 106 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-46 * G.2 * G.4^-7 ] Genus 53 action of group of order 212 via quadrangle group [ 2, 2, 2, 106 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-36 * G.1 * G.2 * G.1^2 * G.4^-16 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3^2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2^2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 53 action of group of order 312 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Largest orientation-preserving group for genus 53 has order 832 ... group action with signature (0: +; [2,4,8]; {-}) Largest group with or without reflections for genus 53 has order 960 ... group action with signature (0; +; [-]; {(2,4,30)}) Largest group with reflections for genus 53 has order 960 ... group action with signature (0; +; [-]; {(2,4,30)}) Largest chiral group for genus 53 has order 832 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 54 has order 416 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 786 : 608 chiral, 178 reflexible, with 57 non-orientable quotient actions Genus 54 actions: Genus 54 action of group of order 456 via triangle group [ 2, 4, 57 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-41 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 54 action of group of order 440 via triangle group [ 2, 4, 110 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-110 ] Genus 54 action of group of order 432 via triangle group [ 2, 4, 216 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-13 * G.1 * G.2^-1 * G.3^-94 ] Genus 54 action of group of order 336 via triangle group [ 2, 6, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^46 * G.2 * G.3^-5 * G.1 * G.3^4 ] Genus 54 action of group of order 304 via triangle group [ 2, 8, 38 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-10 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 54 action of group of order 270 via triangle group [ 2, 10, 135 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-4 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-17 ] Genus 54 action of group of order 264 via triangle group [ 2, 12, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^-1 * G.1 * G.3^10 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 54 action of group of order 280 via triangle group [ 2, 14, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-6 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-10 ] Genus 54 action of group of order 252 via triangle group [ 2, 14, 126 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^3 * G.2^-5 * G.3^3, G.3^-1 * G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 54 action of group of order 240 via triangle group [ 2, 20, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^10 * G.2^-1 * G.3^-1 * G.1 ] Genus 54 action of group of order 240 via triangle group [ 2, 24, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-5 ] Genus 54 action of group of order 234 via triangle group [ 2, 26, 117 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2^-4 * G.3^4 ] Genus 54 action of group of order 240 via triangle group [ 2, 30, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 54 action of group of order 240 via triangle group [ 2, 30, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^7 * G.3^-1 * G.2 * G.3^-1 ] Genus 54 action of group of order 228 via triangle group [ 2, 38, 114 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-8 * G.2^11 * G.3^-3 * G.2^13 * G.3^-1 * G.2 ] Genus 54 action of group of order 228 via triangle group [ 2, 57, 57 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-43 * G.2^11 * G.3^-1 ] Genus 54 action of group of order 222 via triangle group [ 2, 74, 111 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-7 * G.2^11 * G.3^-2 * G.2^14 * G.3^-2 ] Genus 54 action of group of order 218 via triangle group [ 2, 109, 218 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^100 * G.3^-8 * G.2 ] Genus 54 action of group of order 220 via triangle group [ 2, 110, 110 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^9 * G.2^-99 * G.3 ] Genus 54 action of group of order 216 via triangle group [ 2, 216, 216 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^8 * G.2^-98 * G.3 ] Genus 54 action of group of order 327 via triangle group [ 3, 3, 109 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 54 action of group of order 327 via triangle group [ 3, 3, 109 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3^5 * G.2 * G.3^-1 ] Genus 54 action of group of order 220 via triangle group [ 4, 4, 55 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-6 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 ] Genus 54 action of group of order 220 via triangle group [ 4, 4, 55 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.1 * G.3^4 * G.2 * G.1^-1 * G.3^5 ] Genus 54 action of group of order 220 via triangle group [ 4, 4, 55 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-47 * G.1 * G.2 * G.3^-7 ] Genus 54 action of group of order 216 via triangle group [ 4, 4, 108 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-46 * G.1 * G.2^-1 * G.3^-7 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4, G.4^-1 * G.2 * G.4^4 * G.1^2 * G.3 * G.4^-3 * G.2 * G.3 * G.4^-1 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.4 * G.1^2 * G.2 * G.4^-3 * G.1 * G.4, G.4^3 * G.3 * G.4^-2 * G.1 * G.2 * G.4^5 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.1 * G.4^-5, G.4^-1 * G.1 * G.4^4 * G.1^2 * G.3 * G.4^-3 * G.2 * G.4^-2 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-3, G.4 * G.3 * G.4^-4 * G.2^2 * G.1 * G.4^3 * G.2 * G.4^2 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^-5 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-27 * G.2 * G.1 * G.3 * G.4^-27 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-48 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 54 action of group of order 220 via quadrangle group [ 2, 2, 2, 55 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-38 * G.1 * G.2 * G.1 * G.2 * G.4^-15 ] Genus 54 action of group of order 216 via quadrangle group [ 2, 2, 2, 108 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-27 * G.1 * G.4^-27 ] Genus 54 action of group of order 216 via quadrangle group [ 2, 2, 2, 108 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-47 * G.1 * G.3 * G.4^-6 ] Genus 54 action of group of order 216 via quadrangle group [ 2, 2, 2, 108 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-38 * G.1 * G.2 * G.4^-15 ] Largest orientation-preserving group for genus 54 has order 456 ... group action with signature (0: +; [2,4,57]; {-}) Largest group with or without reflections for genus 54 has order 912 ... group action with signature (0; +; [-]; {(2,4,57)}) Largest group with reflections for genus 54 has order 912 ... group action with signature (0; +; [-]; {(2,4,57)}) No chiral group action for genus 54 Largest non-orientable group for non-orientable genus 55 has order 456 ... group action with signature (0; +; [-]; {(2,4,57)}) Check total 38 : 0 chiral, 38 reflexible, with 8 non-orientable quotient actions Genus 55 actions: Genus 55 action of group of order 1296 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 55 action of group of order 864 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-23 * G.1 ] Genus 55 action of group of order 720 via triangle group [ 2, 3, 60 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^4 * G.2^-1 * G.3^-5 ] Genus 55 action of group of order 1296 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 55 action of group of order 1296 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 55 action of group of order 1296 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 55 action of group of order 1296 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-3 ] Genus 55 action of group of order 864 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-1)^6 ] Genus 55 action of group of order 864 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-1)^6 ] Genus 55 action of group of order 720 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3 * G.2^-1 * G.3)^3, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 55 action of group of order 720 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^5, (G.2 * G.3^-4)^2 ] Genus 55 action of group of order 720 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, G.3^10, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 55 action of group of order 648 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2 * G.3^-1)^6, G.3^-8 * G.1 * G.2 * G.3^-7 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-4 * G.2, G.3^3 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 * G.1 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^5 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-6 * G.1 ] Genus 55 action of group of order 576 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 55 action of group of order 504 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2^-1 * G.3)^6, G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 448 via triangle group [ 2, 4, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-41 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 55 action of group of order 448 via triangle group [ 2, 4, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-112 ] Genus 55 action of group of order 440 via triangle group [ 2, 4, 220 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-14 * G.1 * G.2^-1 * G.3^-95 ] Genus 55 action of group of order 810 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 55 action of group of order 648 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-2 ] Genus 55 action of group of order 648 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-2 * G.1 ] Genus 55 action of group of order 648 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 55 action of group of order 648 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^2 * G.2^2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2^-2 * G.3)^3, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2 ] Genus 55 action of group of order 486 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 55 action of group of order 432 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 55 action of group of order 432 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3 * G.2^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 55 action of group of order 432 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^6 * G.2^-1 * G.1 * G.3^5 ] Genus 55 action of group of order 432 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^12 ] Genus 55 action of group of order 378 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 55 action of group of order 360 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-2 ] Genus 55 action of group of order 342 via triangle group [ 2, 6, 57 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^26 * G.2 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3 ] Genus 55 action of group of order 330 via triangle group [ 2, 6, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-27 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 55 action of group of order 504 via triangle group [ 2, 7, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, (G.3 * G.2^-1 * G.3)^3, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2 ] Genus 55 action of group of order 504 via triangle group [ 2, 7, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, (G.2^-2 * G.3)^3, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 55 action of group of order 432 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 324 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^12 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.1 * G.3^8 * G.2^-1 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-6 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-10 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.3^6 * G.2 * G.3^-5 * G.1 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-3)^2 ] Genus 55 action of group of order 288 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 55 action of group of order 264 via triangle group [ 2, 12, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.2 * G.1 * G.3^10 * G.2 * G.3^-9 * G.1 * G.3 ] Genus 55 action of group of order 270 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-3 * G.3^2 * G.2^-6 * G.3^4 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-3 * G.2^8 * G.3^-1 * G.2^2 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^2 * G.3^-1 * G.2^9 * G.3^-3 * G.2 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.2^3 * G.3^-1 * G.2 * G.3^-1 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2 * G.3^-3 * G.2^9 * G.3^-1 * G.2^2 ] Genus 55 action of group of order 288 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^3 * G.3^-3 ] Genus 55 action of group of order 240 via triangle group [ 2, 24, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-12 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 55 action of group of order 240 via triangle group [ 2, 24, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2^-2 * G.3^5 ] Genus 55 action of group of order 252 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-6 * G.3 * G.2^-1 ] Genus 55 action of group of order 240 via triangle group [ 2, 30, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-2 ] Genus 55 action of group of order 234 via triangle group [ 2, 39, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-11 * G.2^9 * G.3^-1 * G.2^2 * G.3^-12 * G.2^3 ] Genus 55 action of group of order 230 via triangle group [ 2, 46, 115 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2, G.2^-11 * G.3^3 * G.2^-6 * G.3^2 * G.2^-1 ] Genus 55 action of group of order 222 via triangle group [ 2, 111, 222 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^101 * G.3^-10 ] Genus 55 action of group of order 224 via triangle group [ 2, 112, 112 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^10 * G.2^-101 ] Genus 55 action of group of order 224 via triangle group [ 2, 112, 112 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-26 * G.2^29 ] Genus 55 action of group of order 220 via triangle group [ 2, 220, 220 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^9 * G.2^-100 ] Genus 55 action of group of order 648 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 55 action of group of order 648 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 55 action of group of order 648 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 648 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 55 action of group of order 648 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 * G.1 ] Genus 55 action of group of order 360 via triangle group [ 3, 3, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 55 action of group of order 360 via triangle group [ 3, 3, 30 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 55 action of group of order 360 via triangle group [ 3, 3, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 351 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 55 action of group of order 351 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 55 action of group of order 333 via triangle group [ 3, 3, 111 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.3^-2 * G.1^2 * G.3^4 * G.2 * G.1 ] Genus 55 action of group of order 333 via triangle group [ 3, 3, 111 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.3^-4 ] Genus 55 action of group of order 648 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 55 action of group of order 648 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 55 action of group of order 648 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 55 action of group of order 648 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.1^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 55 action of group of order 432 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 55 action of group of order 324 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 55 action of group of order 324 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 55 action of group of order 324 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 ] Genus 55 action of group of order 324 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 288 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1 ] Genus 55 action of group of order 288 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-4 * G.1^-1 * G.3^3 * G.2 ] Genus 55 action of group of order 288 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 55 action of group of order 405 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 55 action of group of order 360 via triangle group [ 3, 5, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 55 action of group of order 288 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 55 action of group of order 234 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 55 action of group of order 234 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 ] Genus 55 action of group of order 222 via triangle group [ 3, 6, 74 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 55 action of group of order 222 via triangle group [ 3, 6, 74 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.2 * G.1^-1 * G.3^3 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.2^-9 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-9 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-9 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.2^-9 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^-3, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.1^-1 * G.3^2 * G.2^2 * G.3^-3 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.1^-1 * G.3^2 * G.2^2 * G.3^-3 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.1, G.3^-1 * G.2^3 * G.1 * G.2^-2 * G.3^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.1, G.2^-1 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^-1 * G.2^3 * G.1 * G.2^-2 * G.3^-1 ] Genus 55 action of group of order 243 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2^3 * G.1 * G.2^-2 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.2^-1 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.1^-1 ] Genus 55 action of group of order 432 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.3^-2 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.2^-1 ] Genus 55 action of group of order 360 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.1)^3 ] Genus 55 action of group of order 360 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2)^2, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 324 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, (G.1^-1 * G.3)^6 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^8 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, G.3^8 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^8 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2, G.3^8 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2^-1 * G.3^2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 * G.3 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 55 action of group of order 288 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 55 action of group of order 252 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-56 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^17 * G.2 * G.1^-1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1^-1 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^22 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1^-1 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^16 * G.2^-1 * G.3^-5 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^17 * G.2 * G.1^-1 * G.3^4 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 55 action of group of order 224 via triangle group [ 4, 4, 56 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-21 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-3 ] Genus 55 action of group of order 220 via triangle group [ 4, 4, 110 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-47 * G.1 * G.2^-1 * G.3^-7 ] Genus 55 action of group of order 240 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.3)^6, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.3 * G.4^-1 * G.2 * G.4)^3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3, (G.2 * G.4^-1)^6 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 648 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^27 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.3 * G.1)^9 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.3 * G.1)^9 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^9 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2 * G.4)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.4 * G.2 * G.4)^2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 432 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-5 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-5, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-5, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, (G.1 * G.3)^4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.2 * G.4^-1)^4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.1 * G.3)^4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-5, (G.1 * G.2)^4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-5 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.1 * G.2)^4 ] Genus 55 action of group of order 360 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^2 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.3 * G.1)^9 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^27 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.2 * G.1 * G.3 * G.4^-3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.4^3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4^2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.3 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2 * G.2 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4^3 * G.2 * G.4 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, (G.3 * G.1)^9 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.3 * G.1)^9 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-3 * G.1^2 * G.4 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.3 * G.1)^9 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4^2)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^4 * G.1^2 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-3 * G.1^2 * G.4 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4^2)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.3 * G.1)^9 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, (G.3 * G.1)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^4 * G.1^2 * G.4^4, (G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 55 action of group of order 288 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, (G.1 * G.3)^6 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.3)^6 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 252 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, (G.3 * G.1)^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.3 * G.1)^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.1)^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, (G.2 * G.1)^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-5 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^9 * G.3 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^20 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-8 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-20 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-13 * G.1 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^14 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^7 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-20 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^11 * G.3 * G.2 * G.1 * G.4^8 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^8 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.4^6 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^6, (G.4 * G.2 * G.4^-7 * G.1 * G.4)^2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-3 * G.2 * G.4 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^6, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^3 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.1, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 55 action of group of order 240 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^8 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-9 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.4^-7 * G.2 * G.1 * G.3 * G.2 * G.4^5 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^10 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-9 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-8 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^11 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^11 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4^5 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-13 * G.1 * G.4 * G.1^2 * G.4^4 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.4^7 * G.1 * G.4^-5 * G.2 * G.4^-2 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^12 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-8 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 55 action of group of order 228 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^13 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-56 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-56 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^32 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^17 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-9 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^21 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^16 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-9 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-14 * G.1 * G.4^-1 * G.1 * G.4^-13 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^6 * G.3 * G.4^-10 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.2 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-20 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 * G.2 * G.4^5 * G.3 * G.4^-5 * G.1 * G.4^7 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^7 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4^4 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-8 * G.1 * G.4^-3 * G.1 * G.4^-3 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^6 * G.3 * G.4^-2 * G.1 * G.2 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^6 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^7 * G.3 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.1^2 * G.4^-3 * G.1 * G.4^4 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-7 * G.1 * G.4^-1 * G.1 * G.4^-6 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-2 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^6 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^7 * G.3 * G.1 * G.2 * G.4^6 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.4^2 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.2 * G.4^3 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^7 * G.3 * G.2 * G.4^-3 * G.1 * G.4^3 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.3 * G.1 * G.4^2 * G.3 * G.4^-3 * G.1 * G.4^5 ] Genus 55 action of group of order 224 via quadrangle group [ 2, 2, 2, 56 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 55 action of group of order 220 via quadrangle group [ 2, 2, 2, 110 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-27 * G.2 * G.3 * G.4^-27 ] Genus 55 action of group of order 220 via quadrangle group [ 2, 2, 2, 110 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-48 * G.2 * G.4^-7 ] Genus 55 action of group of order 220 via quadrangle group [ 2, 2, 2, 110 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-38 * G.1 * G.2 * G.1^2 * G.4^-16 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^9, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, (G.4^-1 * G.3)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.4^-1 * G.3)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.4^-1 * G.3)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3 * G.2 * G.3^-1)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.3^-1 * G.1)^3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.3 * G.2 * G.4)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^6, G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 55 action of group of order 324 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.2^-1)^3, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4^-1 ] Largest orientation-preserving group for genus 55 has order 1296 ... group action with signature (0: +; [2,3,12]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 55 has order 2592 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 55 has order 2592 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 55 has order 1296 ... group action with signature (0: +; [2,4,6]; {-}) Largest non-orientable group for non-orientable genus 56 has order 1296 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 1648 : 1128 chiral, 520 reflexible, with 141 non-orientable quotient actions Genus 56 actions: Genus 56 action of group of order 1320 via triangle group [ 2, 3, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 56 action of group of order 1320 via triangle group [ 2, 3, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3 * G.2 * G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.1 * G.3 ] Genus 56 action of group of order 1320 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 56 action of group of order 456 via triangle group [ 2, 4, 114 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-114 ] Genus 56 action of group of order 448 via triangle group [ 2, 4, 224 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-15 * G.1 * G.2^-1 * G.3^-96 ] Genus 56 action of group of order 550 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^4 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 56 action of group of order 550 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 56 action of group of order 550 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 56 action of group of order 550 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 56 action of group of order 660 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2^-2 * G.3)^3, (G.3 * G.2^-1 * G.3)^3, (G.3^-1 * G.2)^5 ] Genus 56 action of group of order 348 via triangle group [ 2, 6, 58 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^39 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 56 action of group of order 336 via triangle group [ 2, 6, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-26 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 56 action of group of order 400 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^10 ] Genus 56 action of group of order 336 via triangle group [ 2, 8, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3^8 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 56 action of group of order 304 via triangle group [ 2, 8, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-10 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 56 action of group of order 330 via triangle group [ 2, 10, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-3 ] Genus 56 action of group of order 330 via triangle group [ 2, 10, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.1 * G.2^-1 * G.3^-1 ] Genus 56 action of group of order 330 via triangle group [ 2, 10, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^5 * G.3^-1 * G.1 * G.3 ] Genus 56 action of group of order 330 via triangle group [ 2, 10, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 56 action of group of order 300 via triangle group [ 2, 10, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-2 * G.1 * G.3^21 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 56 action of group of order 300 via triangle group [ 2, 10, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^10, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-4 ] Genus 56 action of group of order 300 via triangle group [ 2, 10, 30 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^13 * G.2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^5 ] Genus 56 action of group of order 280 via triangle group [ 2, 10, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^2 * G.2^-1 * G.3^-7 * G.1 * G.3 ] Genus 56 action of group of order 288 via triangle group [ 2, 16, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^16, G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 56 action of group of order 252 via triangle group [ 2, 18, 126 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-6 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 56 action of group of order 250 via triangle group [ 2, 25, 50 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2^-1 * G.3^11 * G.2^-4 * G.3 * G.2^-8 ] Genus 56 action of group of order 240 via triangle group [ 2, 30, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-3 * G.2^7 * G.3^-3 * G.2^17 ] Genus 56 action of group of order 238 via triangle group [ 2, 34, 119 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-5 * G.3^3 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 56 action of group of order 240 via triangle group [ 2, 40, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-2 * G.2^4 * G.3^-4 ] Genus 56 action of group of order 232 via triangle group [ 2, 58, 116 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-29 * G.2^12 * G.3^-1 * G.2^13 * G.3^-2 ] Genus 56 action of group of order 226 via triangle group [ 2, 113, 226 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^102 * G.3^-10 * G.2 ] Genus 56 action of group of order 228 via triangle group [ 2, 114, 114 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^11 * G.2^-101 * G.3 ] Genus 56 action of group of order 224 via triangle group [ 2, 224, 224 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^10 * G.2^-100 * G.3 ] Genus 56 action of group of order 660 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 * G.3^-2 ] Genus 56 action of group of order 660 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 56 action of group of order 300 via triangle group [ 3, 4, 20 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^4 * G.2 * G.1^-1 * G.3^5 ] Genus 56 action of group of order 300 via triangle group [ 3, 5, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-5, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 56 action of group of order 240 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.2^-1 * G.3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 56 action of group of order 240 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 56 action of group of order 228 via triangle group [ 4, 4, 57 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-57 ] Genus 56 action of group of order 224 via triangle group [ 4, 4, 112 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-42 * G.1^-1 * G.3^4 * G.2 * G.3^-9 ] Genus 56 action of group of order 240 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 56 action of group of order 240 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3 * G.1^-1 * G.3 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.1^-2 * G.3^2 * G.2 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.1^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.2^2 * G.3^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 56 action of group of order 275 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-2 * G.2 * G.3^-1 * G.2 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-8 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^4 * G.3 * G.4^-5 * G.2 * G.1^2 * G.4^2 * G.3 * G.4^-6 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.4^7 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-5 * G.1 * G.4^2 * G.1^2 * G.2 * G.4^-2 * G.1 * G.4^8 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-3 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^7 * G.2 * G.4 * G.3 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^4 * G.3 * G.4^5 * G.2 * G.1 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-28 * G.2 * G.1 * G.3 * G.4^-28 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-50 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 56 action of group of order 228 via quadrangle group [ 2, 2, 2, 57 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^39 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 56 action of group of order 224 via quadrangle group [ 2, 2, 2, 112 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-28 * G.1 * G.4^-28 ] Genus 56 action of group of order 224 via quadrangle group [ 2, 2, 2, 112 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-49 * G.1 * G.3 * G.4^-6 ] Genus 56 action of group of order 224 via quadrangle group [ 2, 2, 2, 112 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^38 * G.2 * G.1 * G.4^17 ] Largest orientation-preserving group for genus 56 has order 1320 ... group action with signature (0: +; [2,3,12]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 56 has order 2640 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 56 has order 2640 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 56 has order 550 ... group action with signature (0: +; [2,5,10]; {-}) Largest non-orientable group for non-orientable genus 57 has order 1320 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Check total 67 : 20 chiral, 47 reflexible, with 14 non-orientable quotient actions Genus 57 actions: Genus 57 action of group of order 1344 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 1344 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 57 action of group of order 1008 via triangle group [ 2, 3, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.3^7 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^5 ] Genus 57 action of group of order 1344 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 57 action of group of order 576 via triangle group [ 2, 4, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.2, G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 57 action of group of order 576 via triangle group [ 2, 4, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^4 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 57 action of group of order 512 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^6 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 57 action of group of order 512 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-15 * G.1 * G.3^8 * G.2 * G.3^-8 ] Genus 57 action of group of order 512 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.1 * G.3^2 * G.2 * G.3^-5 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 57 action of group of order 512 via triangle group [ 2, 4, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 480 via triangle group [ 2, 4, 60 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-44 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 57 action of group of order 480 via triangle group [ 2, 4, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-14 * G.1 * G.3^8 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 480 via triangle group [ 2, 4, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-45 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 57 action of group of order 464 via triangle group [ 2, 4, 116 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-116 ] Genus 57 action of group of order 456 via triangle group [ 2, 4, 228 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-16 * G.1 * G.2^-1 * G.3^-97 ] Genus 57 action of group of order 640 via triangle group [ 2, 5, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 672 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 672 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 672 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 57 action of group of order 672 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 ] Genus 57 action of group of order 672 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 57 action of group of order 480 via triangle group [ 2, 6, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3^10, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 ] Genus 57 action of group of order 480 via triangle group [ 2, 6, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-4)^2, G.3^10, G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-5 ] Genus 57 action of group of order 384 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2^2 * G.3^-1 * G.2^3 * G.3^-2 * G.2^3 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^-4 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^2 * G.2 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-12 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-12 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.3^-12 ] Genus 57 action of group of order 384 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.3^-6 * G.1 * G.2 * G.3^-5 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^22 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^10 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^30 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-9 ] Genus 57 action of group of order 320 via triangle group [ 2, 8, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 57 action of group of order 304 via triangle group [ 2, 8, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-8 * G.1 * G.3 * G.2 * G.1 * G.3^17 * G.2 * G.1 * G.2^-1 * G.3^-9 ] Genus 57 action of group of order 304 via triangle group [ 2, 8, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-11 * G.1 * G.3^16 * G.2 * G.1 * G.2^-1 * G.3^-9 ] Genus 57 action of group of order 320 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.3, G.2^10, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.3 ] Genus 57 action of group of order 320 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 57 action of group of order 336 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^12 ] Genus 57 action of group of order 336 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^12 ] Genus 57 action of group of order 336 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2^12 ] Genus 57 action of group of order 336 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^12 ] Genus 57 action of group of order 294 via triangle group [ 2, 14, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2^11 * G.3^-1, G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 266 via triangle group [ 2, 14, 133 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^3 * G.2^-5 * G.3^3, G.3^9 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 57 action of group of order 288 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-3 * G.3 * G.2^-1 * G.3 * G.2^-9 * G.3 * G.2^-1 * G.3 ] Genus 57 action of group of order 288 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-3 * G.3 * G.2^-11 * G.3 * G.2^-2 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2^11 * G.3^-3 * G.2^15 * G.3^-2 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-15 * G.3^3 * G.2^-10 * G.3^2 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-2 * G.2 * G.3^-1 * G.2^10 * G.3^-3 * G.2 * G.3^-14 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^2 * G.3^-3 * G.2 * G.3^-1 * G.2^6 * G.3^-2 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-1 * G.3^3 * G.2^-5 * G.3^5 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-2 * G.3 * G.2^-2 * G.3^2 * G.2^-5 * G.3 * G.2^-1 * G.3^2 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^5 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-4 * G.3^3 * G.2^-4 * G.3^5 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^10 * G.3^-3 * G.2^2 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 57 action of group of order 256 via triangle group [ 2, 32, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-4 * G.3 * G.2^8 * G.1 * G.2^-3, G.3^4 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-5 ] Genus 57 action of group of order 240 via triangle group [ 2, 40, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-9 * G.2^11 * G.3^-3 * G.2^16 ] Genus 57 action of group of order 240 via triangle group [ 2, 40, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-8 * G.3^3 * G.2^-6 * G.3^3 ] Genus 57 action of group of order 240 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-46 * G.2^11 * G.3^-1 ] Genus 57 action of group of order 240 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-27 * G.3^3 ] Genus 57 action of group of order 240 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-31 * G.2^12 * G.3^-1 * G.2^16 ] Genus 57 action of group of order 230 via triangle group [ 2, 115, 230 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^103 * G.3^-12 ] Genus 57 action of group of order 232 via triangle group [ 2, 116, 116 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^12 * G.2^-103 ] Genus 57 action of group of order 228 via triangle group [ 2, 228, 228 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^11 * G.2^-102 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 57 action of group of order 672 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 57 action of group of order 504 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 57 action of group of order 672 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3^2 * G.2)^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, (G.1 * G.3^2 * G.2)^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^8, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.1 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-2 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1, G.3^8 ] Genus 57 action of group of order 384 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2, G.3^8 ] Genus 57 action of group of order 336 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^2, (G.1 * G.3 * G.2^2)^2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 ] Genus 57 action of group of order 336 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, G.2^-2 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 57 action of group of order 240 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 57 action of group of order 240 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.3^-1 * G.2^3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2^2 ] Genus 57 action of group of order 336 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 57 action of group of order 336 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3 ] Genus 57 action of group of order 288 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^4 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 288 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^9 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1^-1 * G.3^7 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^5 * G.2 * G.3^-2 * G.1 * G.3^4 * G.2^-1 * G.3^-3 * G.1^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^4 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^5 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-4 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-4 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.2 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^-4 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1^-1 * G.2 * G.3^-3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^16 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^-4 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^5 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.3^-2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1^-1 * G.3^7 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-6 * G.1 * G.3^8 * G.2 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^4 * G.1^-1 * G.3^3 * G.2^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, (G.1 * G.3^-3)^2, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-4 * G.1^-1 * G.3 * G.2 * G.3^-2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^3, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3^2 * G.1^-1 * G.3 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-3)^2 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2^-1 * G.3^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 256 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2 * G.3^-1, G.3^3 * G.2 * G.1^-1 * G.3^4 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^3 * G.2 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-23 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^5 * G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1^-1 * G.3^2 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3 ] Genus 57 action of group of order 240 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-30 ] Genus 57 action of group of order 232 via triangle group [ 4, 4, 58 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-58 ] Genus 57 action of group of order 232 via triangle group [ 4, 4, 58 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.3^7 * G.1^-1 ] Genus 57 action of group of order 232 via triangle group [ 4, 4, 58 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.1^-1 * G.3^6 * G.2^-1 * G.3 ] Genus 57 action of group of order 228 via triangle group [ 4, 4, 114 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-43 * G.1^-1 * G.3^4 * G.2 * G.3^-9 ] Genus 57 action of group of order 320 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 57 action of group of order 240 via triangle group [ 4, 5, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, (G.2 * G.3^-2)^2 ] Genus 57 action of group of order 240 via triangle group [ 4, 5, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2 ] Genus 57 action of group of order 240 via triangle group [ 4, 5, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^-3 * G.1^-1 * G.2 * G.3^-2 ] Genus 57 action of group of order 240 via triangle group [ 4, 5, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.1 * G.3 * G.2)^2, G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 57 action of group of order 240 via triangle group [ 4, 5, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.1 * G.3 * G.2^-1)^2, (G.2 * G.3^-2)^2 ] Genus 57 action of group of order 240 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^6, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-2, G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 ] Genus 57 action of group of order 240 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 672 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^28 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^14 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^14 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^14 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^28 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^14 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 448 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^14 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^14 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3 * G.1 * G.4)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2 * G.4^-1)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1 * G.4)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.1 * G.4)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2 * G.4^-1, (G.4^-1 * G.2 * G.4^-1)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3, (G.3 * G.1 * G.4)^3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 57 action of group of order 288 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6 * G.1^2 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.2 * G.1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6 * G.1^2 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 280 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-10 * G.1^2 * G.4^-6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-3 * G.2 * G.3 * G.4^-3 * G.2 * G.1^2 * G.4^7 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-16 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-3 * G.2 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8 * G.3 * G.1 * G.4 * G.2 * G.4^6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-6 * G.1 * G.4^5 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^11 * G.1^2 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-10 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4^7 * G.3 * G.1^2 * G.2 * G.4^-8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.4^-3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.4^2 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-5, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, (G.1 * G.2)^8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-16 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-16 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^5 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^6 * G.3 * G.4^-1 * G.1 * G.4^-8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-9 * G.2 * G.3 * G.1^2 * G.4^-5 * G.2 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.4^6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-3 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^7 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^9 * G.2 * G.1 * G.2 * G.4^-5 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^4 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^3 * G.2 * G.4^3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^4 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^5 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-3 * G.2 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^2 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^4 * G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8 * G.3 * G.1 * G.4 * G.2 * G.4^6 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^11 * G.1^2 * G.4^5 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^10 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-16 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.3 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-9 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.3 * G.1 * G.2 * G.4^-3 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 57 action of group of order 256 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 * G.2 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.4^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-5 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.4^-5 * G.1 * G.3 * G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^5 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 252 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-5 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^5 * G.3 * G.4^-2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^5 * G.1 * G.4 * G.3 * G.1 * G.4^-8 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^9 * G.3 * G.4^-4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^8 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^8 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^2 * G.3^2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-10 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^9 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^6 * G.3 * G.4^3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-6 * G.1 * G.4^2 * G.2 * G.4^-6 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-4 * G.2 * G.4 * G.1^2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-30 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^19 * G.1 * G.4 * G.3 * G.4^-9 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-16 * G.1^2 * G.4^-14 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^17 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-19 * G.1 * G.2 * G.4^-5 * G.1 * G.4^4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.1 * G.4^15 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-7 * G.2 * G.4 * G.3 * G.4^-10 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^8 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^25 * G.1^2 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-17 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-17 * G.2 * G.4^6 * G.1 * G.4^2 * G.3 * G.4^-4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^23 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-30 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-4 * G.2 * G.3 * G.2 * G.4^6 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^6 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-6 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^23 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^17 * G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-18 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^8 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-4 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^16 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.4^-5 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^16 * G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.4^-2 * G.1 * G.4^5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^18 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-5 * G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^13 * G.3 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-13 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^13 * G.3 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^22 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^23 * G.3 * G.1 * G.4^5 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.2 * G.4^-16 * G.1 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.2 * G.4^-16 * G.1 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-58 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-58 ] Genus 57 action of group of order 232 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^40 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 57 action of group of order 228 via quadrangle group [ 2, 2, 2, 114 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-28 * G.2 * G.3 * G.4^-28 ] Genus 57 action of group of order 228 via quadrangle group [ 2, 2, 2, 114 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-50 * G.2 * G.4^-7 ] Genus 57 action of group of order 228 via quadrangle group [ 2, 2, 2, 114 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^33 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^8, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^8, (G.3 * G.1 * G.3^-1 * G.1)^4, G.2 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4, G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.3^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.3 * G.4^-1)^4, (G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1)^4, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, (G.3 * G.4^-1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.2)^4, (G.1 * G.3^-1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.4 * G.3^-1 * G.2 * G.4^-2, G.4^-5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3^-1 * G.1 * G.4^-2, G.4^-5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.4 * G.3 * G.2 * G.4^2, G.4^-5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-5, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.1 * G.4 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.2 * G.4^2, G.4^-5 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-5, G.2 * G.4^-2 * G.1 * G.4^-2 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-5, G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^2 * G.3 * G.2 * G.4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.4^-5 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.4^-1)^4, G.4 * G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, (G.1 * G.4 * G.2^-1 * G.3)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1)^4, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, (G.2^-1 * G.3 * G.1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^4, (G.2 * G.4^-1)^4, G.3 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^4, (G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3 * G.1)^2, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1)^4, (G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2^-1 * G.3)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4, G.3 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4, G.3 * G.1^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2^-1 * G.1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.2^-1 * G.1)^4, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 57 action of group of order 336 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^-2 * G.2^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4^2 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-5, G.3 * G.2 * G.1 * G.2^-1 * G.4^-2 * G.2^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-2 * G.2^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.2 * G.4^2, G.4^-5, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.2^-1 * G.4^-2 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.4^-5, G.1 * G.4^2 * G.2^-1 * G.4^2 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^2 * G.3 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-2 * G.2^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2 * G.4^-2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1, G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-5, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 57 action of group of order 240 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-5, G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Largest orientation-preserving group for genus 57 has order 1344 ... group action with signature (0: +; [2,3,12]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 57 has order 2688 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 57 has order 2688 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 57 has order 1344 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 58 has order 1008 ... group action with signature (0; +; [-]; {(2,3,18)}) Check total 1600 : 908 chiral, 692 reflexible, with 171 non-orientable quotient actions Genus 58 actions: Genus 58 action of group of order 1368 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 58 action of group of order 1368 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 ] Genus 58 action of group of order 504 via triangle group [ 2, 4, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2^-1 * G.3)^6, G.3^-2 * G.1 * G.3 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-1 ] Genus 58 action of group of order 472 via triangle group [ 2, 4, 118 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-118 ] Genus 58 action of group of order 464 via triangle group [ 2, 4, 232 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-17 * G.1 * G.2^-1 * G.3^-98 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-3 * G.3^-1 * G.2 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.3 * G.2^-2 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 58 action of group of order 684 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 58 action of group of order 456 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 58 action of group of order 456 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 ] Genus 58 action of group of order 456 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.3 * G.2^-2 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 58 action of group of order 456 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 58 action of group of order 360 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-41 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-10 ] Genus 58 action of group of order 360 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-30 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 58 action of group of order 360 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-8 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 58 action of group of order 348 via triangle group [ 2, 6, 174 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^27 * G.2 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^3 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-9, G.2^-2 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-9, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^2 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.2^-9, G.2^-1 * G.3 * G.2^-3 * G.3^3 * G.2^-1 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 58 action of group of order 342 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^-9, G.3^2 * G.2^-3 * G.3 * G.2^-2 * G.3 ] Genus 58 action of group of order 290 via triangle group [ 2, 10, 145 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-3 * G.1 * G.3^17 * G.2 * G.3^-8 ] Genus 58 action of group of order 288 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^-1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 58 action of group of order 288 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-12, G.3^-8 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 58 action of group of order 288 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-6 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 58 action of group of order 270 via triangle group [ 2, 18, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 58 action of group of order 252 via triangle group [ 2, 42, 42 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-3 * G.2^4 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 58 action of group of order 252 via triangle group [ 2, 42, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-15 * G.2^9 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-12 * G.2 ] Genus 58 action of group of order 252 via triangle group [ 2, 42, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-10 * G.2^11 * G.3^-3 * G.2^16 ] Genus 58 action of group of order 240 via triangle group [ 2, 60, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-1 * G.2^8 * G.3^-3 * G.2^17 ] Genus 58 action of group of order 234 via triangle group [ 2, 117, 234 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^104 * G.3^-12 * G.2 ] Genus 58 action of group of order 236 via triangle group [ 2, 118, 118 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^13 * G.2^-103 * G.3 ] Genus 58 action of group of order 232 via triangle group [ 2, 232, 232 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^12 * G.2^-102 * G.3 ] Genus 58 action of group of order 684 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 58 action of group of order 684 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2^2 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 * G.2 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-1 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 58 action of group of order 252 via triangle group [ 3, 6, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.2^2 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 58 action of group of order 252 via triangle group [ 3, 6, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 58 action of group of order 234 via triangle group [ 3, 6, 78 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^4 ] Genus 58 action of group of order 234 via triangle group [ 3, 6, 78 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2 ] Genus 58 action of group of order 252 via triangle group [ 4, 4, 21 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^4 ] Genus 58 action of group of order 236 via triangle group [ 4, 4, 59 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-47 * G.1 * G.2 * G.3^-11 ] Genus 58 action of group of order 232 via triangle group [ 4, 4, 116 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-44 * G.1^-1 * G.3^4 * G.2 * G.3^-9 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 456 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-10 * G.2 * G.1 * G.3 * G.4^-10 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-4 * G.2 * G.4^5 * G.3 * G.1^2 * G.2 * G.4^5 * G.3 * G.4^-5 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-8 * G.1 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^9 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^8 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-4 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^7 * G.2 * G.4^2 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-4 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 58 action of group of order 252 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 58 action of group of order 236 via quadrangle group [ 2, 2, 2, 59 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-29 * G.2 * G.1 * G.3 * G.4^-29 ] Genus 58 action of group of order 236 via quadrangle group [ 2, 2, 2, 59 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-52 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 58 action of group of order 236 via quadrangle group [ 2, 2, 2, 59 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^35 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^17 ] Genus 58 action of group of order 232 via quadrangle group [ 2, 2, 2, 116 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-29 * G.1 * G.4^-29 ] Genus 58 action of group of order 232 via quadrangle group [ 2, 2, 2, 116 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-51 * G.1 * G.3 * G.4^-6 ] Genus 58 action of group of order 232 via quadrangle group [ 2, 2, 2, 116 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^34 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.3^-1 * G.4 * G.2 * G.4)^2, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.3^-1 * G.4 * G.2 * G.4)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.2 * G.1)^3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.2^-1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 58 action of group of order 342 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2 * G.4, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Largest orientation-preserving group for genus 58 has order 1368 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 58 has order 1368 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 58 has order 1008 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest chiral group for genus 58 has order 1368 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 59 has order 456 ... group action with signature (0; +; [2]; {(2,4)}) Check total 477 : 416 chiral, 61 reflexible, with 10 non-orientable quotient actions Genus 59 actions: Genus 59 action of group of order 928 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 59 action of group of order 928 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 59 action of group of order 928 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 59 action of group of order 928 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 59 action of group of order 696 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 59 action of group of order 696 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 59 action of group of order 480 via triangle group [ 2, 4, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-45 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 59 action of group of order 480 via triangle group [ 2, 4, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-120 ] Genus 59 action of group of order 472 via triangle group [ 2, 4, 236 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-18 * G.1 * G.2^-1 * G.3^-99 ] Genus 59 action of group of order 354 via triangle group [ 2, 6, 177 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^47 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2 * G.1 * G.3 * G.2^3 * G.3^-4 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.3 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2^2 * G.1 ] Genus 59 action of group of order 406 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 59 action of group of order 464 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 59 action of group of order 320 via triangle group [ 2, 8, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^11 * G.2 * G.1 * G.3^17 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 59 action of group of order 320 via triangle group [ 2, 8, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^22 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^5 ] Genus 59 action of group of order 348 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 59 action of group of order 348 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 59 action of group of order 280 via triangle group [ 2, 20, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 59 action of group of order 238 via triangle group [ 2, 119, 238 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^105 * G.3^-14 ] Genus 59 action of group of order 240 via triangle group [ 2, 120, 120 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^14 * G.2^-105 ] Genus 59 action of group of order 240 via triangle group [ 2, 120, 120 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^2 * G.3^-29 * G.2^12 * G.3^-1 * G.2^16 ] Genus 59 action of group of order 236 via triangle group [ 2, 236, 236 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^13 * G.2^-104 ] Genus 59 action of group of order 336 via triangle group [ 3, 4, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^3 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 59 action of group of order 336 via triangle group [ 3, 4, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-3 ] Genus 59 action of group of order 336 via triangle group [ 3, 4, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 59 action of group of order 464 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 348 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 348 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3 * G.1^-1 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^10 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^7 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-19 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^47 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-19 * G.1^-1 * G.3^3 * G.2 * G.3^-7 ] Genus 59 action of group of order 240 via triangle group [ 4, 4, 60 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-24 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 59 action of group of order 236 via triangle group [ 4, 4, 118 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-47 * G.1 * G.2^-1 * G.3^-11 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.2^-2)^2, G.2^6, G.3^10 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^3 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1 * G.3^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3 * G.2^2 * G.1^-1 * G.3^3 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.1^-1 * G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 59 action of group of order 240 via triangle group [ 4, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 464 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 59 action of group of order 348 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.2 * G.4 * G.1^2 * G.3 * G.2 * G.4^4 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.4 * G.1^2 * G.2 * G.4^-3 * G.1 * G.4, G.4^6 * G.3 * G.1 * G.2 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.1 * G.4^-5, G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.4^4 * G.3 * G.4 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-3, G.4^6 * G.2 * G.4 * G.2 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-10 * G.1 * G.4^-1 * G.1 * G.4^-9 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^5 * G.3 * G.4^-5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-9 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.2 * G.4^-2 * G.1 * G.4^8 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^3 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^9 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^3 * G.2 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-60 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-60 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.1^2 * G.4^12 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-4 * G.2 * G.4^2 * G.3 * G.4^-12 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^8 * G.3 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^23 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-16 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-15 * G.1 * G.4^-1 * G.1 * G.4^-14 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^13 * G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.4^-9 * G.2 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-16 * G.1 * G.3 * G.1 * G.3 * G.4^-12 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-18 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4^4 * G.2 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^17 * G.3 * G.4^-5 * G.2 * G.1 * G.4^7 ] Genus 59 action of group of order 240 via quadrangle group [ 2, 2, 2, 60 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^9 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4^15 ] Genus 59 action of group of order 236 via quadrangle group [ 2, 2, 2, 118 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-29 * G.2 * G.3 * G.4^-29 ] Genus 59 action of group of order 236 via quadrangle group [ 2, 2, 2, 118 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-52 * G.2 * G.4^-7 ] Genus 59 action of group of order 236 via quadrangle group [ 2, 2, 2, 118 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^35 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Largest orientation-preserving group for genus 59 has order 928 ... group action with signature (0: +; [2,4,8]; {-}) Largest group with or without reflections for genus 59 has order 960 ... group action with signature (0; +; [-]; {(2,4,120)}) Largest group with reflections for genus 59 has order 960 ... group action with signature (0; +; [-]; {(2,4,120)}) Largest chiral group for genus 59 has order 928 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 60 has order 464 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 311 : 222 chiral, 89 reflexible, with 37 non-orientable quotient actions Genus 60 actions: Genus 60 action of group of order 504 via triangle group [ 2, 4, 63 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-47 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 60 action of group of order 488 via triangle group [ 2, 4, 122 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-122 ] Genus 60 action of group of order 480 via triangle group [ 2, 4, 240 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-19 * G.1 * G.2^-1 * G.3^-100 ] Genus 60 action of group of order 372 via triangle group [ 2, 6, 62 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-32 * G.1 * G.3^19 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 60 action of group of order 336 via triangle group [ 2, 8, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^9 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 60 action of group of order 336 via triangle group [ 2, 8, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^26 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 60 action of group of order 320 via triangle group [ 2, 10, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^14 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^10 ] Genus 60 action of group of order 312 via triangle group [ 2, 12, 26 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^10 ] Genus 60 action of group of order 308 via triangle group [ 2, 14, 22 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^8 ] Genus 60 action of group of order 280 via triangle group [ 2, 14, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^3 * G.2^-5 * G.3^3, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 60 action of group of order 288 via triangle group [ 2, 16, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^16, G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 60 action of group of order 264 via triangle group [ 2, 22, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-10 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 60 action of group of order 260 via triangle group [ 2, 26, 130 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-14 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 60 action of group of order 264 via triangle group [ 2, 33, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-1 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 60 action of group of order 248 via triangle group [ 2, 62, 124 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-32 * G.2^12 * G.3^-1 * G.2^15 * G.3^-1 ] Genus 60 action of group of order 252 via triangle group [ 2, 63, 63 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-49 * G.2^11 * G.3^-1 ] Genus 60 action of group of order 246 via triangle group [ 2, 82, 123 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-11 * G.2^11 * G.3^-3 * G.2^15 * G.3^-1 ] Genus 60 action of group of order 242 via triangle group [ 2, 121, 242 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^106 * G.3^-14 * G.2 ] Genus 60 action of group of order 244 via triangle group [ 2, 122, 122 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^15 * G.2^-105 * G.3 ] Genus 60 action of group of order 240 via triangle group [ 2, 240, 240 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^14 * G.2^-104 * G.3 ] Genus 60 action of group of order 372 via triangle group [ 3, 3, 62 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.1 * G.3^6 * G.2 * G.1^-2 * G.3^4 * G.2 ] Genus 60 action of group of order 372 via triangle group [ 3, 3, 62 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-6 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 * G.3^-2 ] Genus 60 action of group of order 244 via triangle group [ 4, 4, 61 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4 * G.2^-1 * G.3^5 * G.1^-1 * G.3 ] Genus 60 action of group of order 244 via triangle group [ 4, 4, 61 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.3^5 * G.2^-1 * G.3^-1 ] Genus 60 action of group of order 244 via triangle group [ 4, 4, 61 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^48 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^11 ] Genus 60 action of group of order 240 via triangle group [ 4, 4, 120 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^47 * G.2 * G.1^-1 * G.3^12 ] Genus 60 action of group of order 244 via quadrangle group [ 2, 2, 2, 61 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-30 * G.2 * G.1 * G.3 * G.4^-30 ] Genus 60 action of group of order 244 via quadrangle group [ 2, 2, 2, 61 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-54 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 60 action of group of order 244 via quadrangle group [ 2, 2, 2, 61 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^49 * G.1^2 * G.4^12 ] Genus 60 action of group of order 240 via quadrangle group [ 2, 2, 2, 120 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-30 * G.1 * G.4^-30 ] Genus 60 action of group of order 240 via quadrangle group [ 2, 2, 2, 120 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-53 * G.1 * G.3 * G.4^-6 ] Genus 60 action of group of order 240 via quadrangle group [ 2, 2, 2, 120 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^47 * G.2 * G.1 * G.4^12 ] Largest orientation-preserving group for genus 60 has order 504 ... group action with signature (0: +; [2,4,63]; {-}) Largest group with or without reflections for genus 60 has order 1008 ... group action with signature (0; +; [-]; {(2,4,63)}) Largest group with reflections for genus 60 has order 1008 ... group action with signature (0; +; [-]; {(2,4,63)}) No chiral group action for genus 60 Largest non-orientable group for non-orientable genus 61 has order 504 ... group action with signature (0; +; [-]; {(2,4,63)}) Check total 32 : 0 chiral, 32 reflexible, with 10 non-orientable quotient actions Genus 61 actions: Genus 61 action of group of order 1440 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 1440 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 1440 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 1440 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^6, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 61 action of group of order 720 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^12 ] Genus 61 action of group of order 720 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^12 ] Genus 61 action of group of order 672 via triangle group [ 2, 4, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 640 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 640 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 61 action of group of order 640 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 640 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 61 action of group of order 576 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^6 ] Genus 61 action of group of order 576 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^5 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3 ] Genus 61 action of group of order 560 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-7 * G.1 * G.3^9 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.3 * G.2^-1 ] Genus 61 action of group of order 560 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-9 ] Genus 61 action of group of order 520 via triangle group [ 2, 4, 52 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-8 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 ] Genus 61 action of group of order 520 via triangle group [ 2, 4, 52 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-7 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-9 ] Genus 61 action of group of order 512 via triangle group [ 2, 4, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-49 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 61 action of group of order 512 via triangle group [ 2, 4, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-12 * G.1 * G.3^11 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 61 action of group of order 496 via triangle group [ 2, 4, 124 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-124 ] Genus 61 action of group of order 488 via triangle group [ 2, 4, 244 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-20 * G.1 * G.2^-1 * G.3^-101 ] Genus 61 action of group of order 600 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-4)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 61 action of group of order 600 via triangle group [ 2, 5, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^10 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.3^2 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, (G.3^-1 * G.2)^5 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 720 via triangle group [ 2, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2 ] Genus 61 action of group of order 480 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2^-1 * G.3^2 * G.2^-2 * G.3^-3 * G.1 ] Genus 61 action of group of order 480 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2 * G.2)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 61 action of group of order 432 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^6 * G.2 * G.1 * G.2 * G.3^-10 ] Genus 61 action of group of order 432 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 432 via triangle group [ 2, 6, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 61 action of group of order 384 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 61 action of group of order 384 via triangle group [ 2, 6, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 378 via triangle group [ 2, 6, 63 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^31 * G.2 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 61 action of group of order 378 via triangle group [ 2, 6, 63 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^8 * G.2 * G.3^-7 * G.1 * G.3 * G.2 * G.3^-3 * G.1 ] Genus 61 action of group of order 378 via triangle group [ 2, 6, 63 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-8 ] Genus 61 action of group of order 366 via triangle group [ 2, 6, 183 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-30 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 360 via triangle group [ 2, 10, 15 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2^-2 * G.3)^3, G.2^10 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 61 action of group of order 360 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 336 via triangle group [ 2, 14, 14 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^4 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-2 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, (G.2^-3 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 320 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 288 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^-1 * G.3^4 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-3 ] Genus 61 action of group of order 288 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-18 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^6 * G.1 * G.2^-4, G.3^8 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-6 * G.3 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-1 * G.2^4)^2, G.2 * G.1 * G.2^-5 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-12 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-1 * G.3 * G.2^10 * G.1, G.3^6 * G.2 * G.3^-5 * G.1 ] Genus 61 action of group of order 288 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 280 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2^-4 * G.3 * G.2^-1 * G.3^4 * G.2^-10 * G.3^4 * G.2^-1 * G.3 ] Genus 61 action of group of order 280 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^5 * G.2^-4 * G.3^2 * G.2^-11 * G.3^4 * G.2^-1 * G.3 ] Genus 61 action of group of order 270 via triangle group [ 2, 30, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-2 * G.3^3 * G.2^-4 * G.3^4 ] Genus 61 action of group of order 270 via triangle group [ 2, 30, 45 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2^7 * G.3^-3 ] Genus 61 action of group of order 270 via triangle group [ 2, 30, 45 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^5 * G.3^-4 ] Genus 61 action of group of order 264 via triangle group [ 2, 33, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-33 ] Genus 61 action of group of order 260 via triangle group [ 2, 52, 52 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3^4 * G.2^-1 * G.3^3 * G.2^-8 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 260 via triangle group [ 2, 52, 52 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-2 * G.3 * G.2^-4 * G.3^2 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^3 ] Genus 61 action of group of order 256 via triangle group [ 2, 64, 64 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-34 * G.2^12 * G.3^-1 * G.2^14 * G.3^-1 * G.2 ] Genus 61 action of group of order 256 via triangle group [ 2, 64, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^2 * G.3^-2 * G.2^10 * G.3^-3 * G.2 * G.3^-13 * G.2 ] Genus 61 action of group of order 256 via triangle group [ 2, 64, 64 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-15 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 256 via triangle group [ 2, 64, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-1 * G.2^10 * G.3^-3 * G.2^17 ] Genus 61 action of group of order 246 via triangle group [ 2, 123, 246 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^107 * G.3^-16 ] Genus 61 action of group of order 248 via triangle group [ 2, 124, 124 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^16 * G.2^-107 ] Genus 61 action of group of order 244 via triangle group [ 2, 244, 244 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^15 * G.2^-106 ] Genus 61 action of group of order 720 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1, (G.3^-1 * G.2)^5 ] Genus 61 action of group of order 720 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.2 * G.3^-1)^4, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 720 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3, (G.3^-1 * G.2)^5 ] Genus 61 action of group of order 720 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.2 * G.1^-1 * G.3)^3, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 360 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 61 action of group of order 300 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 360 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 360 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 61 action of group of order 360 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 61 action of group of order 360 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 360 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 61 action of group of order 336 via triangle group [ 3, 6, 7 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^-1 * G.3 * G.2^2 * G.1 * G.3^3 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-2, G.3 * G.2^2 * G.1^-1 * G.2 * G.3^-1 * G.1 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3, G.3^2 * G.2^2 * G.1^-1 * G.3^3 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^2 * G.2^2 * G.1^-1 * G.3^3 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 61 action of group of order 288 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-2 * G.2)^2 ] Genus 61 action of group of order 360 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 360 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 336 via triangle group [ 4, 4, 7 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 61 action of group of order 320 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3^4 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.1^-1 * G.3^4 * G.2^-1 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^3 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3^3 * G.1^-1 * G.3 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1^-1 * G.3)^6 ] Genus 61 action of group of order 288 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 280 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-5 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 61 action of group of order 280 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^-5 ] Genus 61 action of group of order 260 via triangle group [ 4, 4, 26 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^6 ] Genus 61 action of group of order 260 via triangle group [ 4, 4, 26 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^2 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-32 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3^-5 * G.1 * G.2 * G.1^-1 * G.3^8 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^5 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^5 * G.2 * G.3^-2 * G.1 * G.3^4 * G.2^-1 * G.3^-3 * G.1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^5 * G.2 * G.3^-5 * G.1^-1 * G.3^5 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^18 * G.2^-1 * G.3^-5 * G.1 * G.2 * G.1 * G.3^7 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^5 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^8 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-32 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1^-1 * G.3^7 * G.2^-1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^9 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1^-1 * G.3^7 * G.2^-1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.3^3 * G.2 * G.3^-1 ] Genus 61 action of group of order 256 via triangle group [ 4, 4, 32 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 61 action of group of order 248 via triangle group [ 4, 4, 62 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-48 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 61 action of group of order 244 via triangle group [ 4, 4, 122 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^48 * G.2 * G.1^-1 * G.3^12 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^6, G.3 * G.2 * G.1^-2 * G.3 * G.2^-2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.3^-1 * G.1)^3 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^6, (G.1 * G.3^-1 * G.2^2)^2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3 * G.1^-1, G.3^6 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1 * G.3 * G.1^-1, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.1^-1 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.3^-1 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 61 action of group of order 288 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^6, (G.1 * G.3^-1 * G.2^2)^2 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2^-5 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, (G.1 * G.2^-2)^2, G.2^-5, (G.3^-1 * G.1)^3, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, (G.2^-1 * G.1)^3, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2)^2, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^-5, (G.3^-1 * G.2)^3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1 * G.3^-1 * G.1^-1 * G.3 * G.2, G.2^-5 ] Genus 61 action of group of order 300 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^5, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^5, (G.4^-1 * G.2)^5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^5, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^5, (G.4^-1 * G.2)^5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.3 * G.1)^5, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^5, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^5, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^10, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^10, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^6, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^6, (G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 720 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^10 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^30 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^30 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^20 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^30 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^10 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.3 * G.1)^15 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.1)^5, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, (G.3 * G.1)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 480 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.3 * G.1)^15 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^30 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4^2 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4^2 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1)^5, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-3 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^10 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-7, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-7, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-7, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-7, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-7, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-7, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^-7, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^-7, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-7, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-7, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-7, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-7, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-7, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^-7 ] Genus 61 action of group of order 336 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^10 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^10 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^10 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^10 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, (G.2 * G.1)^5, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.2 * G.1)^5 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4^8, (G.2 * G.1)^5 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, (G.2 * G.1)^5, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, (G.2 * G.1)^5, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.2 * G.1)^5, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4^-3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 320 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, (G.3 * G.1)^5, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4^-3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^10 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^10 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.1)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^10, G.4 * G.1 * G.4 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^10, (G.1 * G.3)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^10, (G.1 * G.2)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^10 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^10 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-3 * G.1 * G.4^3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.2)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.3 * G.1)^15 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 300 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.1 * G.4^-5 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^5 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.3 * G.1 * G.3 * G.4^-5 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-4, G.3 * G.1 * G.3 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-12, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8 * G.1^2 * G.4^4, (G.4^-1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-5 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.2 * G.4^3 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-12, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8 * G.1^2 * G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^3 * G.1 * G.4^3 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-2 * G.1 * G.2 * G.4^5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-4 * G.1 * G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^12 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-12 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, (G.4 * G.2 * G.4^-2 * G.1 * G.4^2)^2, G.4^12 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.1 * G.4^-5 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-5 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.3 * G.1 * G.3 * G.4^-5 * G.1, G.3 * G.1 * G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-4, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-3 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.3 * G.4^-3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-4 * G.2 * G.1 * G.3 * G.4^-4, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^3 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^3 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^12, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^4 * G.2 * G.4 * G.3 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-14, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10 * G.1^2 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, (G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-6 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.2 * G.4^6 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-14 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-14, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^2 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 * G.1 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^10 * G.1^2 * G.4^4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-4 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.4^-5 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^3 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 61 action of group of order 280 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-7 * G.2 * G.4^-4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^5 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-22 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^11 * G.3 * G.4^-1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10 * G.3 * G.4^-5 * G.1 * G.4^-5 * G.2 * G.4 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^8 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^-5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.2 * G.4^8 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-22 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^16 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-7 * G.1 * G.4^3 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^7 * G.2 * G.4^-2 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-15 * G.1 * G.2 * G.3 * G.4^-6 ] Genus 61 action of group of order 264 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.4^-1 * G.1 * G.4^11 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^6 * G.1 * G.4 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-2 * G.2 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4^5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4, (G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^7 * G.3 * G.4^-5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^6 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-5 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-5 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 * G.3 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-9 * G.2 * G.4^-4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^6 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-3 * G.1 * G.4^5 * G.1^2 * G.2 * G.4^-4 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.4^5 * G.1 * G.3 * G.4^-5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-5 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 61 action of group of order 260 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-6 * G.1 * G.4^5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-32 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-10 * G.2 * G.4^4 * G.3 * G.4^-5 * G.2 * G.3 * G.4^-11 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^17 * G.3 * G.1 * G.3 * G.4^-5 * G.1 * G.4^8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-19 * G.2 * G.4^-5 * G.1 * G.3 * G.4^-7 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-16 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^6 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-5 * G.1 * G.4^6 * G.2 * G.1 * G.4^2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-10 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-3 * G.2 * G.4^5 * G.3 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.2 * G.4^7 * G.3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^5 * G.3 * G.4^-3 * G.2 * G.1^2 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-3 * G.1 * G.4^5 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-8 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1^2 * G.4^-3 * G.1 * G.4^2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.4^6 * G.1 * G.3 * G.4^-7 * G.1 * G.4 * G.2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-6 * G.1 * G.2 * G.4^2 * G.2 * G.4^3 * G.2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.4 * G.1 * G.4^-11 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-5 * G.2 * G.4^2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-8 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 * G.3 * G.4^-2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-10 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-2 * G.2 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1^2 * G.4^-5 * G.2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.3 * G.4^-1 * G.1 * G.4^-7 * G.2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-8 * G.2 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-3 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4^-7 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-7 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^6 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^4 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^6 * G.2 * G.1^2 * G.3 * G.4^-6 * G.1 * G.4^3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^5 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^7 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4^5 * G.3 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-4 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^2 * G.3 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.1 * G.4 * G.1 * G.4^-11 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.4^-11 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^27 * G.1^2 * G.4^5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^15 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-13 * G.1 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^6 * G.3 * G.1 * G.4^-9 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-5 * G.1^2 * G.3 * G.4^-6 * G.1 * G.4^3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4^5 * G.3 * G.4^-3 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-10 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^7 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 61 action of group of order 256 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.1 * G.3 * G.4^-6 * G.1 * G.4^2 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^9 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4^6 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-5 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 * G.2 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^12 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-10 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-9 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-15 * G.1 * G.4 * G.1^2 * G.4^4 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^14 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.4^-5 * G.2 * G.1 * G.3 * G.4^-12 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^14 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-8 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 61 action of group of order 252 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-4 * G.2 * G.4^2 * G.3 * G.4^-13 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^8 * G.3 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-6 * G.2 * G.4 * G.3 * G.4^-12 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^8 * G.3 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^26 * G.2 * G.4^5 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^25 * G.3 * G.1 * G.4^5 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-16 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-17 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 * G.2 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-62 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-62 ] Genus 61 action of group of order 248 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.2 * G.1 * G.2 * G.1 * G.4^12 ] Genus 61 action of group of order 244 via quadrangle group [ 2, 2, 2, 122 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-30 * G.2 * G.3 * G.4^-30 ] Genus 61 action of group of order 244 via quadrangle group [ 2, 2, 2, 122 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-54 * G.2 * G.4^-7 ] Genus 61 action of group of order 244 via quadrangle group [ 2, 2, 2, 122 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.2 * G.1 * G.4^12 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.3 * G.4^-1)^4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3^-1 * G.1 * G.3 * G.1)^5, G.2 * G.1^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^10, (G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, (G.1 * G.4 * G.2 * G.3^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^5, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1, (G.4^-1 * G.3)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3^-1 * G.1, G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, (G.1 * G.3^-1)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4^-2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3^-1)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3 * G.2 * G.3^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3^-1 * G.4, G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.4^-1)^4, (G.3 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.3)^4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.1 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2, (G.4^-1 * G.2^-1)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.2^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^5, G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5, G.3 * G.1^-1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.4^-1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^5, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.2^-1 * G.3 * G.1 * G.3 * G.1)^2 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^5 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 61 action of group of order 360 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.1 * G.3)^4, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.1 * G.2^-1 * G.1 * G.2)^3, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.1 * G.2^-1)^6, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4, G.2 * G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 61 action of group of order 288 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 61 has order 1440 ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 61 has order 2880 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest group with reflections for genus 61 has order 2880 ... group action with signature (0; +; [-]; {(2,4,6)}) Largest chiral group for genus 61 has order 1440 ... group action with signature (0: +; [2,4,6]; {-}) Largest non-orientable group for non-orientable genus 62 has order 1440 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 2433 : 1558 chiral, 875 reflexible, with 230 non-orientable quotient actions Genus 62 actions: Genus 62 action of group of order 504 via triangle group [ 2, 4, 126 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-126 ] Genus 62 action of group of order 496 via triangle group [ 2, 4, 248 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-21 * G.1 * G.2^-1 * G.3^-102 ] Genus 62 action of group of order 610 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 62 action of group of order 610 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 62 action of group of order 610 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 62 action of group of order 610 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.2 ] Genus 62 action of group of order 732 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 ] Genus 62 action of group of order 732 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 62 action of group of order 732 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 62 action of group of order 732 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 ] Genus 62 action of group of order 384 via triangle group [ 2, 6, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-33 * G.1 * G.3^17 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-10 ] Genus 62 action of group of order 372 via triangle group [ 2, 6, 186 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-31 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 62 action of group of order 336 via triangle group [ 2, 8, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^32 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^7 ] Genus 62 action of group of order 310 via triangle group [ 2, 10, 155 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^21 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 62 action of group of order 280 via triangle group [ 2, 20, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 62 action of group of order 264 via triangle group [ 2, 44, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-10 * G.3^3 * G.2^-6 * G.3^3 ] Genus 62 action of group of order 250 via triangle group [ 2, 125, 250 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^108 * G.3^-16 * G.2 ] Genus 62 action of group of order 252 via triangle group [ 2, 126, 126 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^17 * G.2^-107 * G.3 ] Genus 62 action of group of order 248 via triangle group [ 2, 248, 248 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^16 * G.2^-106 * G.3 ] Genus 62 action of group of order 366 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 62 action of group of order 366 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 62 action of group of order 366 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 ] Genus 62 action of group of order 366 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 62 action of group of order 252 via triangle group [ 4, 4, 63 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-49 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 62 action of group of order 248 via triangle group [ 4, 4, 124 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-48 * G.1 * G.2^-1 * G.3^-13 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1^2 * G.3^2 * G.1^-1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.1 * G.2^-2 * G.1^2 * G.2^-1 * G.1 * G.2^-1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1^2 * G.2^-2 * G.1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.1^-2 * G.2^-1 * G.1^2 * G.3 * G.2^-1 * G.3 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2^-1 ] Genus 62 action of group of order 305 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.1^-2 * G.2^-1 * G.1^2 * G.2^-1 * G.3^2 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.2 * G.3 * G.1 * G.4^-5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-31 * G.2 * G.1 * G.3 * G.4^-31 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-56 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 62 action of group of order 252 via quadrangle group [ 2, 2, 2, 63 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.1^2 * G.4^15 ] Genus 62 action of group of order 248 via quadrangle group [ 2, 2, 2, 124 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-31 * G.1 * G.4^-31 ] Genus 62 action of group of order 248 via quadrangle group [ 2, 2, 2, 124 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-55 * G.1 * G.3 * G.4^-6 ] Genus 62 action of group of order 248 via quadrangle group [ 2, 2, 2, 124 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^49 * G.1^2 * G.2 * G.1 * G.4^12 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3^2 * G.1 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3^2 * G.1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 62 action of group of order 366 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 62 has order 732 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 62 has order 1008 ... group action with signature (0; +; [-]; {(2,4,126)}) Largest group with reflections for genus 62 has order 1008 ... group action with signature (0; +; [-]; {(2,4,126)}) Largest chiral group for genus 62 has order 732 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 63 has order 366 ... group action with signature (0; +; [2,3]; {(1)}) Check total 297 : 264 chiral, 33 reflexible, with 8 non-orientable quotient actions Genus 63 actions: Genus 63 action of group of order 1488 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 ] Genus 63 action of group of order 1488 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 63 action of group of order 528 via triangle group [ 2, 4, 66 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-50 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 63 action of group of order 512 via triangle group [ 2, 4, 128 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-49 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 63 action of group of order 512 via triangle group [ 2, 4, 128 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-128 ] Genus 63 action of group of order 504 via triangle group [ 2, 4, 252 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-22 * G.1 * G.2^-1 * G.3^-103 ] Genus 63 action of group of order 504 via triangle group [ 2, 7, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 63 action of group of order 504 via triangle group [ 2, 7, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^-7, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 63 action of group of order 504 via triangle group [ 2, 7, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, (G.2 * G.3^-2 * G.2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 63 action of group of order 352 via triangle group [ 2, 8, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^30 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3 ] Genus 63 action of group of order 352 via triangle group [ 2, 8, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^23 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 63 action of group of order 336 via triangle group [ 2, 8, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-13 * G.1 * G.3^17 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 63 action of group of order 336 via triangle group [ 2, 8, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-12 * G.1 * G.3^18 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 ] Genus 63 action of group of order 336 via triangle group [ 2, 12, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.2 * G.1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3^2 ] Genus 63 action of group of order 312 via triangle group [ 2, 12, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^4 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^5 ] Genus 63 action of group of order 320 via triangle group [ 2, 16, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.3 * G.2^10 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^10 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3 ] Genus 63 action of group of order 320 via triangle group [ 2, 16, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 63 action of group of order 288 via triangle group [ 2, 16, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-5 * G.3^3)^2, G.3^3 * G.2 * G.3^-2 * G.1 * G.3^6 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 63 action of group of order 288 via triangle group [ 2, 16, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-5 * G.3^3)^2, G.3^-3 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 63 action of group of order 280 via triangle group [ 2, 20, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-8 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 63 action of group of order 280 via triangle group [ 2, 35, 35 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^-3 * G.3^15 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-10 * G.3^2 ] Genus 63 action of group of order 280 via triangle group [ 2, 35, 35 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^17 * G.2^-15 ] Genus 63 action of group of order 266 via triangle group [ 2, 38, 133 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-7 * G.3^3 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 63 action of group of order 264 via triangle group [ 2, 44, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-13 * G.2^11 * G.3^-3 * G.2^13 * G.3^-2 * G.2 ] Genus 63 action of group of order 264 via triangle group [ 2, 66, 66 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-52 * G.2^11 * G.3^-1 ] Genus 63 action of group of order 258 via triangle group [ 2, 86, 129 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-12 * G.2^11 * G.3^-3 * G.2^16 ] Genus 63 action of group of order 254 via triangle group [ 2, 127, 254 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^109 * G.3^-18 ] Genus 63 action of group of order 256 via triangle group [ 2, 128, 128 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^18 * G.2^-109 ] Genus 63 action of group of order 256 via triangle group [ 2, 128, 128 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-34 * G.2^12 * G.3^-1 * G.2^15 * G.3^-1 ] Genus 63 action of group of order 252 via triangle group [ 2, 252, 252 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^17 * G.2^-108 ] Genus 63 action of group of order 744 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 63 action of group of order 744 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 63 action of group of order 381 via triangle group [ 3, 3, 127 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 63 action of group of order 381 via triangle group [ 3, 3, 127 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 63 action of group of order 372 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 63 action of group of order 372 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 63 action of group of order 264 via triangle group [ 4, 4, 33 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-26 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-26 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^21 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^8 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-21 * G.1^-1 * G.3^3 * G.2 * G.3^-7 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-21 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-50 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 63 action of group of order 256 via triangle group [ 4, 4, 64 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-21 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 63 action of group of order 252 via triangle group [ 4, 4, 126 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-49 * G.1 * G.2^-1 * G.3^-13 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 496 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 63 action of group of order 372 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^-27 * G.2 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-20 * G.2 * G.4^6 * G.1 * G.4^2 * G.3 * G.4^-4 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-16 * G.2 * G.1 * G.3 * G.4^-16 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^20 * G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^26 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-20 * G.1 * G.4^7 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^21 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^-26 * G.1 * G.4 * G.2 * G.4^-5 ] Genus 63 action of group of order 264 via quadrangle group [ 2, 2, 2, 33 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-19 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.4^-6 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-64 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-64 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.2 * G.1 * G.2 * G.1 * G.4^14 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-11 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^25 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^16 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^13 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-16 * G.1 * G.4^-1 * G.1 * G.4^-15 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-10 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-10 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^17 * G.3 * G.1 * G.3 * G.4^-8 * G.1 * G.4^5 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^10 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-24 * G.1 * G.2 * G.4^5 * G.3 * G.4^-2 ] Genus 63 action of group of order 256 via quadrangle group [ 2, 2, 2, 64 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-18 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-8 ] Genus 63 action of group of order 252 via quadrangle group [ 2, 2, 2, 126 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-31 * G.2 * G.3 * G.4^-31 ] Genus 63 action of group of order 252 via quadrangle group [ 2, 2, 2, 126 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-56 * G.2 * G.4^-7 ] Genus 63 action of group of order 252 via quadrangle group [ 2, 2, 2, 126 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^48 * G.1^2 * G.2 * G.1 * G.4^14 ] Largest orientation-preserving group for genus 63 has order 1488 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 63 has order 1488 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 63 has order 1056 ... group action with signature (0; +; [-]; {(2,4,66)}) Largest chiral group for genus 63 has order 1488 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 64 has order 528 ... group action with signature (0; +; [-]; {(2,4,66)}) Check total 292 : 214 chiral, 78 reflexible, with 29 non-orientable quotient actions Genus 64 actions: Genus 64 action of group of order 1512 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 1512 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 1134 via triangle group [ 2, 3, 18 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 1134 via triangle group [ 2, 3, 18 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 1008 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 1008 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 1008 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 1008 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 64 action of group of order 882 via triangle group [ 2, 3, 42 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^10 * G.2 * G.3^-9 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 64 action of group of order 648 via triangle group [ 2, 4, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-18 ] Genus 64 action of group of order 648 via triangle group [ 2, 4, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2 * G.3^-1)^6, G.1 * G.3^8 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 64 action of group of order 520 via triangle group [ 2, 4, 130 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-130 ] Genus 64 action of group of order 512 via triangle group [ 2, 4, 256 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-23 * G.1 * G.2^-1 * G.3^-104 ] Genus 64 action of group of order 720 via triangle group [ 2, 5, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^8 ] Genus 64 action of group of order 720 via triangle group [ 2, 5, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^8, (G.3 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.2^2 * G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^3 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 64 action of group of order 756 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-3 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-4 * G.2 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 64 action of group of order 504 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-8 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-4 * G.1 * G.3^6 * G.2 * G.3^-3 * G.1 * G.2 * G.3^-9 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-13 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-6 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 432 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^6 * G.2^2 * G.1 * G.3^5 ] Genus 64 action of group of order 420 via triangle group [ 2, 6, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^2 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 64 action of group of order 420 via triangle group [ 2, 6, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 64 action of group of order 420 via triangle group [ 2, 6, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 420 via triangle group [ 2, 6, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 64 action of group of order 396 via triangle group [ 2, 6, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-2 * G.1 * G.3^9 * G.2 * G.1 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-4 ] Genus 64 action of group of order 396 via triangle group [ 2, 6, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-33 * G.1 * G.3^18 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 396 via triangle group [ 2, 6, 66 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-66 ] Genus 64 action of group of order 384 via triangle group [ 2, 6, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^50 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-2 * G.2^2 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.3^-2 * G.2 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2 * G.3^-2 * G.2^3 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 64 action of group of order 432 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 340 via triangle group [ 2, 10, 34 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^18 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^3 ] Genus 64 action of group of order 320 via triangle group [ 2, 10, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^19 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 64 action of group of order 360 via triangle group [ 2, 12, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 360 via triangle group [ 2, 12, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3 * G.2^-4 * G.3^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^3 * G.2^3 * G.3^-1 * G.2^2 * G.1 ] Genus 64 action of group of order 336 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-2, G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 64 action of group of order 336 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-2, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.2 ] Genus 64 action of group of order 336 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 336 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3 ] Genus 64 action of group of order 312 via triangle group [ 2, 12, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^14 * G.2 * G.3^-3 * G.1 * G.3^8 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, (G.2^-4 * G.3^4 * G.2^-1)^2 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3^-6 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4, G.2^-6 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-2 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-12 * G.3 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-11 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-9 * G.3 * G.2^-1 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^5 * G.2^-5 * G.3 * G.2^-3 * G.3^2 * G.2^-1 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-2 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3^-3 * G.2, G.3^2 * G.2^-3 * G.3 * G.2^-8 * G.3^2 * G.2^-1 * G.3 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-3 * G.3^3 * G.2^-6 * G.3^2 * G.2^-2 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-6 * G.3, G.2^3 * G.1 * G.2^-5 * G.3 * G.2^5 * G.1 * G.2^-2 * G.3 * G.2 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-3 * G.3 * G.2^-2 * G.3 * G.2^-6 * G.3 * G.2^-1 * G.3^3 ] Genus 64 action of group of order 324 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 64 action of group of order 288 via triangle group [ 2, 18, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-3 * G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4, G.2^-6 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 64 action of group of order 294 via triangle group [ 2, 21, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-16 ] Genus 64 action of group of order 294 via triangle group [ 2, 21, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-13 ] Genus 64 action of group of order 294 via triangle group [ 2, 21, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3 * G.2^7 * G.1 * G.2^-4, G.2^-4 * G.3 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-8 ] Genus 64 action of group of order 280 via triangle group [ 2, 28, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^6 * G.2^-4 * G.3^4 ] Genus 64 action of group of order 272 via triangle group [ 2, 34, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-2 * G.2^11 * G.3^-3 * G.2^17 * G.3^-1 ] Genus 64 action of group of order 270 via triangle group [ 2, 45, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-16 * G.2^9 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-13 * G.2 ] Genus 64 action of group of order 264 via triangle group [ 2, 66, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-36 * G.2^12 * G.3^-1 * G.2^15 * G.3^-1 ] Genus 64 action of group of order 258 via triangle group [ 2, 129, 258 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^110 * G.3^-18 * G.2 ] Genus 64 action of group of order 260 via triangle group [ 2, 130, 130 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^19 * G.2^-109 * G.3 ] Genus 64 action of group of order 256 via triangle group [ 2, 256, 256 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^18 * G.2^-108 * G.3 ] Genus 64 action of group of order 756 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 64 action of group of order 756 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 64 action of group of order 567 via triangle group [ 3, 3, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 64 action of group of order 504 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 441 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 441 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 64 action of group of order 441 via triangle group [ 3, 3, 21 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3^6 * G.2^-1 * G.3^-5 ] Genus 64 action of group of order 441 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 441 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 64 action of group of order 387 via triangle group [ 3, 3, 129 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.1^-1 * G.3^4 * G.2 ] Genus 64 action of group of order 387 via triangle group [ 3, 3, 129 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^-5 ] Genus 64 action of group of order 504 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 504 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 360 via triangle group [ 3, 4, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.1 * G.3^-4, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 64 action of group of order 324 via triangle group [ 3, 4, 36 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^5 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2 * G.1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-2 * G.2^2 * G.1^-1 * G.3^2 * G.2^2 * G.3^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.1, (G.1 * G.3 * G.2^2)^2 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.2^6, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 64 action of group of order 336 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 324 via triangle group [ 3, 6, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3 * G.2^-3 * G.1^-1 * G.2^-2 * G.3 * G.2^-1 ] Genus 64 action of group of order 324 via triangle group [ 3, 6, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 64 action of group of order 324 via triangle group [ 3, 6, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 64 action of group of order 324 via triangle group [ 3, 6, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.2^-1 * G.3 * G.2^-3 * G.1^-1 * G.2^-2 * G.3 * G.2^-1 ] Genus 64 action of group of order 324 via triangle group [ 3, 6, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 294 via triangle group [ 3, 6, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^2 * G.2^2 * G.1^-1 * G.3^4 ] Genus 64 action of group of order 294 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.1 ] Genus 64 action of group of order 294 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 64 action of group of order 294 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-2 * G.3^-1 ] Genus 64 action of group of order 294 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 64 action of group of order 258 via triangle group [ 3, 6, 86 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-3 * G.2 * G.1^-1 * G.2 * G.3^-3 ] Genus 64 action of group of order 258 via triangle group [ 3, 6, 86 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^4 ] Genus 64 action of group of order 324 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-9 ] Genus 64 action of group of order 324 via triangle group [ 4, 4, 9 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.3^4 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2 * G.3^-6 * G.1 * G.3^4 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-51 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-5 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-5 * G.1 * G.3^-1 * G.2 * G.3^-2 ] Genus 64 action of group of order 260 via triangle group [ 4, 4, 65 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-4 * G.1^-1 * G.3^6 * G.2^-1 ] Genus 64 action of group of order 256 via triangle group [ 4, 4, 128 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-50 * G.1 * G.2^-1 * G.3^-13 ] Genus 64 action of group of order 360 via triangle group [ 4, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 64 action of group of order 360 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 64 action of group of order 360 via triangle group [ 4, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2 ] Genus 64 action of group of order 360 via triangle group [ 4, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.1)^3, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 504 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-3 * G.1^2 * G.4 * G.2 * G.4^-2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-3 * G.1^2 * G.4 * G.2 * G.4^-2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^3 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^8, G.4^-3 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^2 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3 * G.1 * G.4)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2 * G.4^-1)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.2 * G.4^-3 * G.2 * G.1 * G.4^3 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.2 * G.4^3 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.3 * G.4^-3 * G.1 * G.4^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.2 * G.1 * G.4)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-3 * G.1 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4^3 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.3 * G.4^-3 * G.1 * G.4^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^8, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3, (G.3 * G.1 * G.4)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2 * G.4^-1, (G.4^-1 * G.2 * G.4^-1)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.1 * G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-3 * G.1 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.1 * G.4)^3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 64 action of group of order 336 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-9, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-9, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, (G.1 * G.3)^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-9, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-9, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 64 action of group of order 324 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 64 action of group of order 294 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-4 * G.2 * G.4^4 ] Genus 64 action of group of order 294 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 64 action of group of order 294 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.4^-3 * G.1 * G.2 * G.4^4 ] Genus 64 action of group of order 294 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-4 * G.1 * G.4^4 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^5 * G.1 * G.4^-5, G.4^-2 * G.2 * G.4^4 * G.1 * G.3 * G.4^-6 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.4 * G.1^2 * G.2 * G.4^-3 * G.1 * G.4, G.4^-7 * G.1 * G.4^-4 * G.1 * G.4^-2 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^5)^2, G.4^-2 * G.1 * G.4^4 * G.1 * G.4^-7 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.4^2 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-3, G.4 * G.3 * G.4^-5 * G.1 * G.2 * G.4^2 * G.2 * G.4^3 * G.2 * G.4 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^6 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.4^2 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-32 * G.2 * G.1 * G.3 * G.4^-32 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-58 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 64 action of group of order 260 via quadrangle group [ 2, 2, 2, 65 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^54 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 64 action of group of order 256 via quadrangle group [ 2, 2, 2, 128 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-32 * G.1 * G.4^-32 ] Genus 64 action of group of order 256 via quadrangle group [ 2, 2, 2, 128 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-57 * G.1 * G.3 * G.4^-6 ] Genus 64 action of group of order 256 via quadrangle group [ 2, 2, 2, 128 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^49 * G.2 * G.1 * G.4^14 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1)^2, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2 * G.3 * G.2^-1 * G.3)^3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 64 action of group of order 378 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Largest orientation-preserving group for genus 64 has order 1512 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 64 has order 2016 ... group action with signature (0; +; [-]; {(2,3,24)}) Largest group with reflections for genus 64 has order 2016 ... group action with signature (0; +; [-]; {(2,3,24)}) Largest chiral group for genus 64 has order 1512 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 65 has order 720 ... group action with signature (0; +; [-]; {(2,5,8)}) Check total 1017 : 798 chiral, 219 reflexible, with 54 non-orientable quotient actions Genus 65 actions: Genus 65 action of group of order 3072 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 ] Genus 65 action of group of order 1920 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 2560 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2^-1 * G.3)^8, G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2, G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-2)^4, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 1536 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 1024 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^4, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 * G.1, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.2, (G.2 * G.3^-2)^4, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 * G.1, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-2)^4, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^4, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^12 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4, G.3^12, G.3^-3 * G.1 * G.3 * G.2^-2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-5)^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 640 via triangle group [ 2, 4, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 640 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.1 * G.3^4 * G.2^-1 * G.3^-5 ] Genus 65 action of group of order 640 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^4 * G.2^-1 * G.3^-5, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 640 via triangle group [ 2, 4, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2, G.3^-2 * G.1 * G.3^10 * G.2 * G.3^-7 ] Genus 65 action of group of order 640 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^7 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-9 * G.1 ] Genus 65 action of group of order 576 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-21 * G.1 * G.3^11 * G.2^-1 * G.3^-3 ] Genus 65 action of group of order 576 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^6 * G.2 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 65 action of group of order 576 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-17 * G.1 * G.3^11 * G.2^-1 * G.3^-7 ] Genus 65 action of group of order 544 via triangle group [ 2, 4, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-53 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 65 action of group of order 528 via triangle group [ 2, 4, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-132 ] Genus 65 action of group of order 520 via triangle group [ 2, 4, 260 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-24 * G.1 * G.2^-1 * G.3^-105 ] Genus 65 action of group of order 1280 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.3^-1 * G.2)^5, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 960 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, (G.3^-1 * G.2)^5, (G.2 * G.3^-2)^4, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 960 via triangle group [ 2, 5, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, (G.3^-1 * G.2)^5, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 960 via triangle group [ 2, 5, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, (G.3^-1 * G.2)^5, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-2 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^6, (G.2 * G.3^-1)^6 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 ] Genus 65 action of group of order 672 via triangle group [ 2, 6, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-3 * G.1 * G.2 * G.3^-3, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 480 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-2 * G.2^2 * G.1 * G.3^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 480 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^3 * G.3^-2 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 480 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 408 via triangle group [ 2, 6, 51 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^8 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 390 via triangle group [ 2, 6, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^52 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.2 * G.3^-2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.3^8, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.3^8 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 512 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^4 * G.2 * G.3^-2 * G.1 * G.3^5 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^8, (G.2 * G.3^-1 * G.2^2)^2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^-4 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^-3 * G.3^-2 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-11 * G.1 * G.3^6 * G.2 * G.3^-6 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.1 * G.3^9 * G.2 * G.1 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^6 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^5 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 352 via triangle group [ 2, 8, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^32 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3 ] Genus 65 action of group of order 352 via triangle group [ 2, 8, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^23 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3^11 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.3^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-5 * G.3^-5, G.2^-1 * G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-5 * G.3^-5, G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-5 * G.3^-5, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.3^2 * G.2^3 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, (G.2 * G.3^-1 * G.2)^4 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-1 * G.2 * G.3^-2 * G.2, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^12 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 336 via triangle group [ 2, 12, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^12 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^3 ] Genus 65 action of group of order 312 via triangle group [ 2, 12, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.1 * G.3^7 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-13 ] Genus 65 action of group of order 336 via triangle group [ 2, 14, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-4, G.3 * G.2^5 * G.3^-1 * G.2^2 * G.1 ] Genus 65 action of group of order 336 via triangle group [ 2, 14, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2^4 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 320 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-2 ] Genus 65 action of group of order 320 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-3 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.2^5 * G.3^-4 ] Genus 65 action of group of order 320 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2^5 * G.3^-4, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 65 action of group of order 320 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^3 * G.2^-8 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 320 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-2 * G.3^3 * G.2^-12 * G.3 * G.2^-2 ] Genus 65 action of group of order 286 via triangle group [ 2, 22, 143 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^7 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 280 via triangle group [ 2, 28, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-16 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 65 action of group of order 288 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-36 ] Genus 65 action of group of order 288 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-11 * G.3^2 * G.2^-1 ] Genus 65 action of group of order 288 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-19 * G.3^3 * G.2^-10 * G.3^2 ] Genus 65 action of group of order 270 via triangle group [ 2, 54, 135 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-15 * G.3^3 * G.2^-6 * G.3^2 * G.2^-1 ] Genus 65 action of group of order 272 via triangle group [ 2, 68, 68 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-38 * G.2^12 * G.3^-1 * G.2^16 * G.3^-1 ] Genus 65 action of group of order 262 via triangle group [ 2, 131, 262 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^111 * G.3^-20 ] Genus 65 action of group of order 264 via triangle group [ 2, 132, 132 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^20 * G.2^-111 ] Genus 65 action of group of order 260 via triangle group [ 2, 260, 260 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^19 * G.2^-110 ] Genus 65 action of group of order 1536 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, (G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1)^2 ] Genus 65 action of group of order 960 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.3^-1 * G.2)^3, (G.1 * G.2^-1 * G.3^-1)^4 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^6 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.3 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 768 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.3^-3)^2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^-2 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1)^4, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.1^-1 * G.3 * G.2^-2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.3^2)^2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, G.3^6, (G.2 * G.1^-1 * G.3)^3 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3^2 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 65 action of group of order 336 via triangle group [ 3, 7, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-7, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3 * G.2)^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2)^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, (G.1 * G.3^2 * G.2^-1)^2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.3^2 * G.2)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2, G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.3^2 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, (G.1 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.3^6 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, G.3^6, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, (G.1 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, (G.1 * G.3 * G.1^-1 * G.2^-1)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^2 * G.2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.1 * G.3^2 * G.2)^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^6, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^6, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^10 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, (G.1 * G.3^-3)^2, G.3^10 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, (G.2 * G.3^-2)^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-2 * G.1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-2 * G.1 * G.3^2, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, (G.2 * G.3^-2)^2, G.3^10 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1 * G.3^2, (G.2 * G.3^-1)^4 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1 * G.3^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3^10 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, (G.1 * G.2^-1)^4 ] Genus 65 action of group of order 320 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, (G.1 * G.2^-1)^4 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-3 * G.1^-1 * G.3^7 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.3^8 * G.2 * G.1 * G.3^2 * G.2 * G.3^-3 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-3 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^6 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3^5 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^10 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^9 * G.2^-1 * G.3^-4 * G.1 * G.3^4 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^9 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^6 ] Genus 65 action of group of order 288 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^-6 * G.1 ] Genus 65 action of group of order 272 via triangle group [ 4, 4, 34 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-22 * G.1 * G.3^4 * G.2 * G.3^-7 ] Genus 65 action of group of order 272 via triangle group [ 4, 4, 34 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 65 action of group of order 272 via triangle group [ 4, 4, 34 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4 * G.2^-1 * G.3^2 * G.1^-1 * G.3^3 ] Genus 65 action of group of order 264 via triangle group [ 4, 4, 66 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-52 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 65 action of group of order 260 via triangle group [ 4, 4, 130 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-51 * G.1 * G.2^-1 * G.3^-13 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3)^3, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3, (G.1 * G.2)^8 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^8 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^8 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.2)^6 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.2)^6, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 768 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^16 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^16 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^16 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^16 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^32 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^8 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^32 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 512 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^16 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^16 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1 * G.4)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^2 * G.3^2 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.4^3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.2)^6 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.3 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4^2 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4^-1)^4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, (G.1 * G.3)^8 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, (G.1 * G.3)^8 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^5, G.4^10, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^5, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^10, G.1 * G.4^-5 * G.1 * G.4^5 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.1 * G.4^2 * G.2, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.1 * G.4^-1 * G.2 * G.4^-2, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^10, G.1 * G.4^-5 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^10, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5, G.4^10, G.1 * G.4^-5 * G.1 * G.4^5 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.4^-5 * G.1 * G.4^5, G.1 * G.3 * G.2 * G.4^4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.2 * G.1)^5, G.4^10, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^-3, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^10 ] Genus 65 action of group of order 320 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^14 * G.1^2 * G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-11 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^4 * G.3 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-18, G.1 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-11 * G.2 * G.3 * G.1^2 * G.4^-5 * G.2 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^8 * G.1 * G.4 * G.3 * G.4^-7 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.2 * G.4^2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-18 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^6 * G.3 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^7 * G.1^2 * G.4^11 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.1 * G.4 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-5 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.4^6 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-11 * G.1 * G.2 * G.3 * G.4^-6 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^9 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^8 * G.1 * G.4 * G.3 * G.4^-7 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^9 * G.3 * G.4^-1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-18 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^14 * G.1^2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-10 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-4 * G.1 * G.4^-5 * G.1 * G.2 * G.3 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^4 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^7 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4^-5 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^4 * G.3 * G.1 * G.4 * G.1 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.3 * G.4^-4 * G.2 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 * G.3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-4 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4^8 * G.3 * G.1^2 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-5 * G.2 * G.4^9 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-18 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-10 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^4 * G.3 * G.4^-7 * G.1 * G.4 * G.2 * G.4^5 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-11 * G.1^2 * G.4^-7 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-6 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-3 * G.1 * G.4^2 * G.2 * G.4^-3 * G.1 * G.4^4 ] Genus 65 action of group of order 288 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.3 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-9 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 * G.3 * G.4^-3 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 * G.3 * G.4^-4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^13 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-13 * G.2 * G.4^-4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^10 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-2 * G.1 * G.4^6 * G.3 * G.1^2 * G.4 * G.2 * G.4^-3 * G.1 * G.4^2 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.4^9 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-10 * G.1 * G.4^5 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-34 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-12 * G.2 * G.4^4 * G.3 * G.4^-5 * G.2 * G.3 * G.4^-11 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-13 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-13 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^11 * G.3 * G.4^-9 * G.1 * G.2 * G.4^13 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-18 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-13 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-17 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^14 * G.3 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-29 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 272 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-15 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-15 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-12 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^8 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.4^-12 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^8 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-28 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^27 * G.3 * G.1 * G.4^5 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-7 * G.1 * G.4^13 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4^13 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-13 * G.1 * G.4^-2 * G.1 * G.4^-7 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^9 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4^5 * G.3 * G.4^-4 * G.2 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.1 * G.4^6 * G.3 * G.1 * G.4 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-9 * G.1 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9 * G.1 * G.4^2 * G.1^2 * G.2 * G.4^-2 * G.1 * G.4^7 * G.2 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-6 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^7 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-8 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 * G.2 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-66 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-66 ] Genus 65 action of group of order 264 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-66 ] Genus 65 action of group of order 260 via quadrangle group [ 2, 2, 2, 130 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-32 * G.2 * G.3 * G.4^-32 ] Genus 65 action of group of order 260 via quadrangle group [ 2, 2, 2, 130 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-58 * G.2 * G.4^-7 ] Genus 65 action of group of order 260 via quadrangle group [ 2, 2, 2, 130 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^38 * G.2 * G.4^-15 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4 * G.3^-1 * G.4, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, (G.4^-1 * G.3)^3, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.2)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3 * G.2 * G.3^-1)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3 * G.1 * G.3^-1 * G.1)^8, G.2 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^4, G.3^-1 * G.4^-1 * G.1^2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.3^-1)^4, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^16, G.2 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^4, G.2 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3^-1 * G.4^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.3 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1)^4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.2^-1)^3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2)^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.1 * G.3)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.2^-1 * G.4^-1)^8, G.3 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, (G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2 * G.4^-1 * G.2 * G.1 * G.3)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.3)^4, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, (G.2^-1 * G.1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.1)^4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, (G.2^-1 * G.1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^8 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.3)^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.2^-1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^4, (G.1 * G.2^-1 * G.3)^3, G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, (G.2^-1 * G.1)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-1)^8, G.3 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.2^-1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, (G.2^-1 * G.3)^4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 65 action of group of order 384 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Largest orientation-preserving group for genus 65 has order 3072 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 65 has order 6144 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 65 has order 6144 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 65 has order 1536 ... group action with signature (0: +; [2,4,6]; {-}) Largest non-orientable group for non-orientable genus 66 has order 960 ... group action with signature (0; +; [-]; {(2,5,6)}) Check total 2906 : 1514 chiral, 1392 reflexible, with 212 non-orientable quotient actions Genus 66 actions: Genus 66 action of group of order 1014 via triangle group [ 2, 3, 26 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-25 * G.1 ] Genus 66 action of group of order 600 via triangle group [ 2, 4, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1 * G.3^6 ] Genus 66 action of group of order 552 via triangle group [ 2, 4, 69 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-53 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 66 action of group of order 536 via triangle group [ 2, 4, 134 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-134 ] Genus 66 action of group of order 528 via triangle group [ 2, 4, 264 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-25 * G.1 * G.2^-1 * G.3^-106 ] Genus 66 action of group of order 408 via triangle group [ 2, 6, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^54 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^6 ] Genus 66 action of group of order 400 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^-5 * G.1 * G.2^-3 * G.3^-4 ] Genus 66 action of group of order 368 via triangle group [ 2, 8, 46 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-23 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.2^-1 * G.3^-11 ] Genus 66 action of group of order 450 via triangle group [ 2, 9, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^10 ] Genus 66 action of group of order 350 via triangle group [ 2, 10, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^22 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^3 ] Genus 66 action of group of order 330 via triangle group [ 2, 10, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-5 * G.1 * G.3^20 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 66 action of group of order 338 via triangle group [ 2, 13, 26 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-13 ] Genus 66 action of group of order 336 via triangle group [ 2, 14, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^6 * G.2 * G.1 * G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^6 ] Genus 66 action of group of order 308 via triangle group [ 2, 14, 154 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-2 * G.2^9 * G.3^-2, G.3^-1 * G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 66 action of group of order 286 via triangle group [ 2, 26, 143 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^6 * G.2^-3 * G.1 * G.3^4 ] Genus 66 action of group of order 300 via triangle group [ 2, 30, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2^-1 * G.3^13 * G.2^-1 * G.3 * G.2^-11 * G.3 * G.2^-1 * G.3 ] Genus 66 action of group of order 300 via triangle group [ 2, 30, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-16 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 66 action of group of order 300 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^-8 * G.3^-1 * G.2 * G.1, G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 66 action of group of order 276 via triangle group [ 2, 46, 138 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-14 * G.2^11 * G.3^-3 * G.2^15 * G.3^-1 * G.2 ] Genus 66 action of group of order 272 via triangle group [ 2, 68, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2^12 * G.3^-3 * G.2^18 ] Genus 66 action of group of order 276 via triangle group [ 2, 69, 69 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-55 * G.2^11 * G.3^-1 ] Genus 66 action of group of order 266 via triangle group [ 2, 133, 266 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^112 * G.3^-20 * G.2 ] Genus 66 action of group of order 268 via triangle group [ 2, 134, 134 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^21 * G.2^-111 * G.3 ] Genus 66 action of group of order 264 via triangle group [ 2, 264, 264 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^20 * G.2^-110 * G.3 ] Genus 66 action of group of order 507 via triangle group [ 3, 3, 13 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-13 ] Genus 66 action of group of order 399 via triangle group [ 3, 3, 133 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 66 action of group of order 399 via triangle group [ 3, 3, 133 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 ] Genus 66 action of group of order 399 via triangle group [ 3, 3, 133 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3^-5 ] Genus 66 action of group of order 399 via triangle group [ 3, 3, 133 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^7 * G.2 * G.1^-2 * G.3^4 ] Genus 66 action of group of order 300 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.3^3 ] Genus 66 action of group of order 300 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-9 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 * G.3^-1 ] Genus 66 action of group of order 300 via triangle group [ 4, 4, 15 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^4 * G.2 * G.3^-5 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 66 action of group of order 268 via triangle group [ 4, 4, 67 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^56 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^9 ] Genus 66 action of group of order 264 via triangle group [ 4, 4, 132 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-52 * G.1 * G.2^-1 * G.3^-13 ] Genus 66 action of group of order 312 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 ] Genus 66 action of group of order 312 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 66 action of group of order 312 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 66 action of group of order 312 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^5 * G.1 * G.4^-5, G.4^-7 * G.2 * G.1 * G.4^5 * G.3 * G.4^-2 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-2 * G.2 * G.4^2 * G.1 * G.4^4 * G.1^2 * G.3 * G.4^-6 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^5)^2, G.4^-8 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^8 * G.3 * G.1^2 * G.2 * G.1 * G.4^6 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^3 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4 * G.2 * G.4 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^15 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 66 action of group of order 300 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 66 action of group of order 268 via quadrangle group [ 2, 2, 2, 67 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-33 * G.2 * G.1 * G.3 * G.4^-33 ] Genus 66 action of group of order 268 via quadrangle group [ 2, 2, 2, 67 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-60 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 66 action of group of order 268 via quadrangle group [ 2, 2, 2, 67 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-49 * G.1 * G.2 * G.1 * G.2 * G.4^-16 ] Genus 66 action of group of order 264 via quadrangle group [ 2, 2, 2, 132 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-33 * G.1 * G.4^-33 ] Genus 66 action of group of order 264 via quadrangle group [ 2, 2, 2, 132 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-59 * G.1 * G.3 * G.4^-6 ] Genus 66 action of group of order 264 via quadrangle group [ 2, 2, 2, 132 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-56 * G.1 * G.2 * G.4^-9 ] Largest orientation-preserving group for genus 66 has order 1014 ... group action with signature (0: +; [2,3,26]; {-}) Largest group with or without reflections for genus 66 has order 2028 ... group action with signature (0; +; [-]; {(2,3,26)}) Largest group with reflections for genus 66 has order 2028 ... group action with signature (0; +; [-]; {(2,3,26)}) Largest chiral group for genus 66 has order 312 ... group action with signature (0: +; [4,6,6]; {-}) Largest non-orientable group for non-orientable genus 67 has order 552 ... group action with signature (0; +; [-]; {(2,4,69)}) Check total 53 : 4 chiral, 49 reflexible, with 8 non-orientable quotient actions Genus 67 actions: Genus 67 action of group of order 576 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2 * G.3^-1)^6, G.3^-3 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2 * G.3^-6 ] Genus 67 action of group of order 576 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^3 ] Genus 67 action of group of order 544 via triangle group [ 2, 4, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-53 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 67 action of group of order 544 via triangle group [ 2, 4, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-136 ] Genus 67 action of group of order 536 via triangle group [ 2, 4, 268 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-26 * G.1 * G.2^-1 * G.3^-107 ] Genus 67 action of group of order 432 via triangle group [ 2, 6, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-7 * G.1 ] Genus 67 action of group of order 414 via triangle group [ 2, 6, 69 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-36 * G.1 * G.3^18 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 67 action of group of order 402 via triangle group [ 2, 6, 201 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-35 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 67 action of group of order 480 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-4)^2, G.3^10 ] Genus 67 action of group of order 480 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^10, G.3^-2 * G.2 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 67 action of group of order 432 via triangle group [ 2, 9, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 67 action of group of order 432 via triangle group [ 2, 9, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 ] Genus 67 action of group of order 432 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 67 action of group of order 336 via triangle group [ 2, 12, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 67 action of group of order 330 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^-15 ] Genus 67 action of group of order 330 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^-15 ] Genus 67 action of group of order 330 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.3 * G.2^-9 * G.3 * G.2^-4 ] Genus 67 action of group of order 330 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-4, G.2^-15 ] Genus 67 action of group of order 320 via triangle group [ 2, 16, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 67 action of group of order 320 via triangle group [ 2, 16, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.3 * G.2^10 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2^5 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-5 ] Genus 67 action of group of order 288 via triangle group [ 2, 36, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^2 * G.3^-3 * G.2 * G.3^-1 * G.2^10 * G.3^-3 * G.2 * G.3^-13 * G.2^2 ] Genus 67 action of group of order 288 via triangle group [ 2, 36, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-3 * G.2^11 * G.3^-3 * G.2^19 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-19 * G.2^9 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-14 * G.2 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^6 * G.1 * G.2^-4, G.2^-3 * G.3^5 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-8 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-15 * G.2^11 * G.3^-3 * G.2^18 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-12 * G.3^3 * G.2^-6 * G.3^3 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2^2 * G.3^-3 * G.2^3)^2 ] Genus 67 action of group of order 288 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3 * G.2^-5 * G.3^-1 * G.1 * G.3^3 ] Genus 67 action of group of order 270 via triangle group [ 2, 135, 270 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^113 * G.3^-22 ] Genus 67 action of group of order 272 via triangle group [ 2, 136, 136 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^22 * G.2^-113 ] Genus 67 action of group of order 272 via triangle group [ 2, 136, 136 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-37 * G.2^12 * G.3^-1 * G.2^17 ] Genus 67 action of group of order 268 via triangle group [ 2, 268, 268 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^21 * G.2^-112 ] Genus 67 action of group of order 288 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^3 * G.2 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 67 action of group of order 288 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^4 ] Genus 67 action of group of order 288 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 67 action of group of order 288 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 67 action of group of order 288 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^8, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.3^2 * G.2 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^4 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^3 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3^3 * G.1^-1 * G.3 ] Genus 67 action of group of order 288 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1^-1 * G.3)^6 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^4 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^3 * G.1^-1 * G.3^4 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-23 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-23 * G.1^-1 * G.3^3 * G.2 * G.3^-7 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-4 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^54 * G.2 * G.1 * G.3^13 ] Genus 67 action of group of order 272 via triangle group [ 4, 4, 68 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-22 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 67 action of group of order 268 via triangle group [ 4, 4, 134 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^56 * G.2 * G.1^-1 * G.3^10 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, (G.2 * G.3^-2)^2, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2, G.2^6, (G.1 * G.3^-1 * G.2)^2 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.3^-1 * G.2)^2, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.3^-1 * G.2)^2 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.2 * G.1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-1)^4, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.3^-2, G.2^6, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.1^-1 * G.2 * G.1^-2 * G.3 * G.2^2, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, (G.2 * G.3^-1)^4, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 ] Genus 67 action of group of order 288 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.2^6, G.3^8 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^22 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^33 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 528 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^33 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 396 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 352 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^9 * G.1^2 * G.4^5, G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^3 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2, G.1 * G.3 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 67 action of group of order 308 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-24 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-5 * G.2 * G.3 * G.4^-11 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^11 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 * G.3 * G.4^-9 * G.1 * G.2 * G.4^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^12 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-10 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-24 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^8 * G.2 * G.4^-3 * G.1 * G.2 * G.1^2 * G.4^-2 * G.1 * G.4^9 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.4^-7 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.4^5 * G.2 * G.4^5 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-24 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^-9 * G.1 * G.2 * G.4^8 * G.3 * G.4^-6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^20 * G.1^2 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^7 * G.3 * G.1 * G.4 * G.3 * G.4^-6 * G.1 * G.4^8 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^8 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-11 * G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-7 * G.1 * G.2 * G.1 * G.4^7 * G.2 * G.4^-8 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-11 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^10 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-12 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^3 * G.1 * G.3 * G.4^-6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-5 * G.2 * G.4^3 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-3 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-5 * G.1 * G.2 * G.4 * G.3 * G.4^-4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.1 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-4 * G.1 * G.4^2 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.4^3 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-4 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-4 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-5 * G.1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^4 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^6 * G.1 * G.4^-1 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-2 * G.1 * G.2 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.4^-4 * G.1 * G.2 * G.4 * G.2 * G.4^4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.1 * G.4^-1 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.3 * G.1 * G.4^-5 * G.1 * G.2 * G.4 * G.3 * G.4^-4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-4 * G.1 * G.4^2 * G.3 * G.4^-5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-9 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, (G.1 * G.3)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.1 * G.3 * G.2 * G.4^4, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^3 * G.3 * G.2 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.3)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^3 * G.2)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, (G.1 * G.4^3 * G.2)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4^3 * G.3 * G.2 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 67 action of group of order 288 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^11 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4^6 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^5 * G.3 * G.4^-5 * G.1 * G.2 * G.1^2 * G.3 * G.4^-11 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^12 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-11 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-10 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-19 * G.2 * G.4^-4 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^4 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^13 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^16 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^7 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 * G.4^9 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-16 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^9 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 67 action of group of order 276 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-12 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-68 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-68 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-50 * G.1 * G.2 * G.1 * G.2 * G.4^-16 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-9 * G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^14 * G.3 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^27 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-14 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-13 * G.1 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-17 * G.1 * G.4^-1 * G.1 * G.4^-16 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-11 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-10 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-13 * G.1 * G.4^5 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-13 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^11 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^10 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^11 * G.3 * G.4^-9 * G.1 * G.4^5 * G.2 * G.4^8 ] Genus 67 action of group of order 272 via quadrangle group [ 2, 2, 2, 68 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-18 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^3 * G.2 * G.4^-5 ] Genus 67 action of group of order 268 via quadrangle group [ 2, 2, 2, 134 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-33 * G.2 * G.3 * G.4^-33 ] Genus 67 action of group of order 268 via quadrangle group [ 2, 2, 2, 134 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-60 * G.2 * G.4^-7 ] Genus 67 action of group of order 268 via quadrangle group [ 2, 2, 2, 134 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-50 * G.1 * G.2 * G.4^-16 ] Largest orientation-preserving group for genus 67 has order 576 ... group action with signature (0: +; [2,4,48]; {-}) Largest group with or without reflections for genus 67 has order 1152 ... group action with signature (0; +; [-]; {(2,4,48)}) Largest group with reflections for genus 67 has order 1152 ... group action with signature (0; +; [-]; {(2,4,48)}) Largest chiral group for genus 67 has order 528 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 68 has order 528 ... group action with signature (0; +; [-]; {(2,2,2,4)}) ... group action with signature (0; +; [2]; {(2,4)}) Check total 979 : 680 chiral, 299 reflexible, with 89 non-orientable quotient actions Genus 68 actions: Genus 68 action of group of order 552 via triangle group [ 2, 4, 138 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-138 ] Genus 68 action of group of order 544 via triangle group [ 2, 4, 272 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-27 * G.1 * G.2^-1 * G.3^-108 ] Genus 68 action of group of order 804 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 68 action of group of order 804 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 68 action of group of order 804 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 ] Genus 68 action of group of order 804 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 68 action of group of order 420 via triangle group [ 2, 6, 70 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^56 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^6 ] Genus 68 action of group of order 408 via triangle group [ 2, 6, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-33 * G.1 * G.3 * G.2 * G.1 * G.3^18 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 68 action of group of order 368 via triangle group [ 2, 8, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-23 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-10 ] Genus 68 action of group of order 360 via triangle group [ 2, 10, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-6 * G.1 * G.3^12 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-4 ] Genus 68 action of group of order 340 via triangle group [ 2, 10, 170 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-4 * G.1 * G.3^19 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 ] Genus 68 action of group of order 336 via triangle group [ 2, 12, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^18 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 68 action of group of order 306 via triangle group [ 2, 18, 153 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-5 * G.3^4)^2, G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-6 ] Genus 68 action of group of order 320 via triangle group [ 2, 20, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 68 action of group of order 288 via triangle group [ 2, 36, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-3 * G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4, G.2^-6 * G.3^3 * G.2^-4 * G.3^5 ] Genus 68 action of group of order 280 via triangle group [ 2, 70, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-39 * G.2^12 * G.3^-1 * G.2^17 ] Genus 68 action of group of order 274 via triangle group [ 2, 137, 274 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^114 * G.3^-22 * G.2 ] Genus 68 action of group of order 276 via triangle group [ 2, 138, 138 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^23 * G.2^-113 * G.3 ] Genus 68 action of group of order 272 via triangle group [ 2, 272, 272 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^22 * G.2^-112 * G.3 ] Genus 68 action of group of order 402 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 68 action of group of order 402 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 68 action of group of order 402 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 ] Genus 68 action of group of order 402 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 ] Genus 68 action of group of order 336 via triangle group [ 3, 7, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^-7, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 68 action of group of order 336 via triangle group [ 3, 7, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 68 action of group of order 276 via triangle group [ 4, 4, 69 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^69 ] Genus 68 action of group of order 272 via triangle group [ 4, 4, 136 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^54 * G.2 * G.1^-1 * G.3^13 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-11 * G.2 * G.3 * G.1 * G.4^-11 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-5 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^2 * G.3 * G.4^-9 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-10 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.1^2 * G.4^-2 * G.1 * G.4^9 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^6 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^6 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^9 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-34 * G.2 * G.1 * G.3 * G.4^-34 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-62 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 68 action of group of order 276 via quadrangle group [ 2, 2, 2, 69 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-51 * G.1 * G.2 * G.1 * G.4^16 * G.2 ] Genus 68 action of group of order 272 via quadrangle group [ 2, 2, 2, 136 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-34 * G.1 * G.4^-34 ] Genus 68 action of group of order 272 via quadrangle group [ 2, 2, 2, 136 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-61 * G.1 * G.3 * G.4^-6 ] Genus 68 action of group of order 272 via quadrangle group [ 2, 2, 2, 136 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-51 * G.1 * G.2 * G.4^-16 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 68 action of group of order 402 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Largest orientation-preserving group for genus 68 has order 804 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 68 has order 1104 ... group action with signature (0; +; [-]; {(2,4,138)}) Largest group with reflections for genus 68 has order 1104 ... group action with signature (0; +; [-]; {(2,4,138)}) Largest chiral group for genus 68 has order 804 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 69 has order 420 ... group action with signature (0; +; [-]; {(2,6,70)}) Check total 311 : 272 chiral, 39 reflexible, with 9 non-orientable quotient actions Genus 69 actions: Genus 69 action of group of order 2448 via triangle group [ 2, 3, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 2448 via triangle group [ 2, 3, 9 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 69 action of group of order 2448 via triangle group [ 2, 3, 9 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 1088 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 69 action of group of order 1088 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 69 action of group of order 1088 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 69 action of group of order 1088 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 69 action of group of order 816 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 816 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 69 action of group of order 680 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 680 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-20 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-56 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-5 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3^6 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-57 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 69 action of group of order 576 via triangle group [ 2, 4, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-17 * G.1 * G.3^10 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 69 action of group of order 560 via triangle group [ 2, 4, 140 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-140 ] Genus 69 action of group of order 552 via triangle group [ 2, 4, 276 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-28 * G.1 * G.2^-1 * G.3^-109 ] Genus 69 action of group of order 480 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-5 ] Genus 69 action of group of order 480 via triangle group [ 2, 6, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 69 action of group of order 480 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 480 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4 ] Genus 69 action of group of order 480 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3 * G.2)^2, (G.2 * G.3^-4)^2, G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-3 * G.1 * G.3^10 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-11 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-17 * G.1 * G.3^16 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-5 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.3^4 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^33 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^10 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 * G.1 * G.3^5 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 69 action of group of order 384 via triangle group [ 2, 8, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^9 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 368 via triangle group [ 2, 8, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-16 * G.1 * G.3^17 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 69 action of group of order 368 via triangle group [ 2, 8, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-15 * G.1 * G.3^18 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 408 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 69 action of group of order 408 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-4 * G.1 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, (G.3 * G.2^-1 * G.3)^3, G.2^12, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-4 * G.1 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.3^2 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2^12 ] Genus 69 action of group of order 384 via triangle group [ 2, 12, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 69 action of group of order 336 via triangle group [ 2, 12, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^9 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-13 * G.1 ] Genus 69 action of group of order 322 via triangle group [ 2, 14, 161 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^7 * G.3^-3, G.3^-1 * G.1 * G.3^10 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 320 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^4 * G.2^-5 * G.3^4, G.3^9 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 320 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 69 action of group of order 320 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 69 action of group of order 320 via triangle group [ 2, 16, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-3 * G.3^4 * G.2^-5 * G.3^4, G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 69 action of group of order 340 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 69 action of group of order 340 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 69 action of group of order 320 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2^-1 * G.3^4 * G.2^-11 * G.3^3 ] Genus 69 action of group of order 320 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2^-15 * G.3 * G.2^-3 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^2 * G.3^-58 * G.2^11 * G.3^-1 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-33 * G.3^3 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-1 * G.3 * G.2^-13 * G.3 * G.2^-1 * G.3 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^2 * G.2^-15 * G.3 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-40 * G.2^12 * G.3^-1 * G.2^17 * G.3^-1 ] Genus 69 action of group of order 288 via triangle group [ 2, 72, 72 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-19 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 69 action of group of order 282 via triangle group [ 2, 94, 141 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-16 * G.2^11 * G.3^-3 * G.2^15 * G.3^-2 ] Genus 69 action of group of order 278 via triangle group [ 2, 139, 278 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^115 * G.3^-24 ] Genus 69 action of group of order 280 via triangle group [ 2, 140, 140 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^24 * G.2^-115 ] Genus 69 action of group of order 276 via triangle group [ 2, 276, 276 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^23 * G.2^-114 ] Genus 69 action of group of order 417 via triangle group [ 3, 3, 139 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 ] Genus 69 action of group of order 417 via triangle group [ 3, 3, 139 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.3^5 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 384 via triangle group [ 3, 4, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 69 action of group of order 384 via triangle group [ 3, 4, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^3 * G.2 * G.1^-1 * G.3^4, G.1^-1 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 384 via triangle group [ 3, 4, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 69 action of group of order 384 via triangle group [ 3, 4, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 69 action of group of order 544 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-2 ] Genus 69 action of group of order 408 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 69 action of group of order 408 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 69 action of group of order 340 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 69 action of group of order 340 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^-3 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-3 * G.1^-1 * G.3^7 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^9 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 * G.3^7 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^5 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3^5 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^29 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^6 * G.2 * G.3^-5 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^5 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2 * G.3^-4 * G.1^-1 * G.3^4 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-24 * G.1 * G.3^4 * G.2 * G.3^-7 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^10 * G.2^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^28 * G.2 * G.3^-7 * G.1 ] Genus 69 action of group of order 288 via triangle group [ 4, 4, 36 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^29 * G.2^-1 * G.3^-2 * G.1 * G.3^4 ] Genus 69 action of group of order 280 via triangle group [ 4, 4, 70 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.2 * G.3^-5 * G.1 * G.3^5 ] Genus 69 action of group of order 280 via triangle group [ 4, 4, 70 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-3 * G.1^-1 * G.3 ] Genus 69 action of group of order 280 via triangle group [ 4, 4, 70 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-70 ] Genus 69 action of group of order 276 via triangle group [ 4, 4, 138 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^60 * G.2 * G.1^-1 * G.3^8 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^-5, (G.1 * G.3^-2)^2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^-5, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^-5, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-5, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^-5, (G.2 * G.3^-1)^4 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, G.2^2 * G.1^-2 * G.3 * G.2 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^-5, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1, (G.1 * G.2^-1 * G.3 * G.2^-1)^2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.2 * G.3^-2)^2, G.3 * G.2^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.2 * G.3^-2)^2, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-5, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2, (G.1 * G.3 * G.2^-2)^2 ] Genus 69 action of group of order 320 via triangle group [ 4, 5, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^-5, G.2 * G.1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^34 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^34 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 544 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 408 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.4^-3 * G.3 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 69 action of group of order 340 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-36 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-24 * G.2 * G.1 * G.4 * G.3 * G.4^-10 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^19 * G.3 * G.1 * G.4 * G.3 * G.4^-6 * G.1 * G.4^8 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^15 * G.2 * G.4^-8 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^10 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-16 * G.2 * G.4^-5 * G.1 * G.3 * G.4^-14 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-19 * G.1 * G.2 * G.1 * G.4^7 * G.2 * G.4^-8 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-5 * G.1 * G.2 * G.3 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^10 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-9 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^10 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.3 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-10 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-5 * G.1 * G.2 * G.3 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^7 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-9 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.4^5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^10 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-1 * G.1 * G.4^5 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-11 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.4^8 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-11 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^3 * G.3 * G.4^-3 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-11 * G.2 * G.4 * G.3 * G.4^-11 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 * G.3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-31 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^18 * G.2 * G.4^-1 * G.1 * G.4^14 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^10 * G.3 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^4 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-8 * G.2 * G.3 * G.1 * G.4^-9 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-13 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^13 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.2 * G.4^-6 * G.1 * G.4^2 * G.2 * G.1 * G.4^6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-36 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^28 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-22 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4^4 * G.3 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9 * G.1 * G.4^-1 * G.2 * G.4^3 * G.3 * G.1 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^6 * G.3 * G.2 * G.4^4 * G.1 * G.3 * G.2 * G.4^6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-6 * G.2 * G.4^3 * G.3 * G.4^-2 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^23 * G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^29 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-23 * G.1 * G.4^7 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-6 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^4 * G.3 * G.4^-7 * G.1 * G.2 * G.4^5 * G.2 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^24 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-22 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.4^-6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^27 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^11 * G.3 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-4 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4^4 * G.3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-4 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^5 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-5 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^3 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^5 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 69 action of group of order 288 via quadrangle group [ 2, 2, 2, 36 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-8 * G.2 * G.4 * G.3 * G.4^-13 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^8 * G.3 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-23 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 * G.3 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-30 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^29 * G.3 * G.1 * G.4^5 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^18 * G.2 * G.4^-1 * G.1 * G.4^15 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^8 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^14 * G.2 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^5 * G.1 * G.4^-5, G.4^-1 * G.2 * G.4^5 * G.3 * G.1 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-2 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.4 * G.1^2 * G.2 * G.4^-3 * G.1 * G.4, G.2 * G.4^6 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^5)^2, G.4^-5 * G.1 * G.4^2 * G.1 * G.4^-7 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4, G.4^5 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-3, G.4^8 * G.2 * G.4^2 * G.2 * G.4^4 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4 * G.2 * G.4^-6 * G.1 * G.4^5 * G.3 * G.4 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-70 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-70 ] Genus 69 action of group of order 280 via quadrangle group [ 2, 2, 2, 70 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^52 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 69 action of group of order 276 via quadrangle group [ 2, 2, 2, 138 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-34 * G.2 * G.3 * G.4^-34 ] Genus 69 action of group of order 276 via quadrangle group [ 2, 2, 2, 138 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-62 * G.2 * G.4^-7 ] Genus 69 action of group of order 276 via quadrangle group [ 2, 2, 2, 138 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-50 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 * G.2 ] Largest orientation-preserving group for genus 69 has order 2448 ... group action with signature (0: +; [2,3,9]; {-}) Largest group with or without reflections for genus 69 has order 4896 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest group with reflections for genus 69 has order 4896 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest chiral group for genus 69 has order 1088 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 70 has order 2448 ... group action with signature (0; +; [-]; {(2,3,9)}) Check total 666 : 452 chiral, 214 reflexible, with 60 non-orientable quotient actions Genus 70 actions: Genus 70 action of group of order 568 via triangle group [ 2, 4, 142 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-142 ] Genus 70 action of group of order 560 via triangle group [ 2, 4, 280 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-29 * G.1 * G.2^-1 * G.3^-110 ] Genus 70 action of group of order 660 via triangle group [ 2, 5, 11 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-5 * G.1 * G.2 * G.3^-5, (G.2 * G.3^-1)^6 ] Genus 70 action of group of order 660 via triangle group [ 2, 5, 11 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.3 * G.2^-1 * G.3)^3, (G.3^-1 * G.2)^5 ] Genus 70 action of group of order 432 via triangle group [ 2, 6, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^8 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 70 action of group of order 432 via triangle group [ 2, 6, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^57 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 70 action of group of order 432 via triangle group [ 2, 6, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 70 action of group of order 432 via triangle group [ 2, 6, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^52 * G.2^-1 * G.1 * G.3^19 ] Genus 70 action of group of order 420 via triangle group [ 2, 6, 210 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^56 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 70 action of group of order 360 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^15 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 70 action of group of order 360 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-11 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 ] Genus 70 action of group of order 360 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-5, G.2^12 ] Genus 70 action of group of order 336 via triangle group [ 2, 12, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-9 * G.1 * G.3^4 * G.2^-1 * G.3^-14 ] Genus 70 action of group of order 352 via triangle group [ 2, 16, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-5 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 70 action of group of order 308 via triangle group [ 2, 22, 154 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1, G.2^-8 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 70 action of group of order 290 via triangle group [ 2, 58, 145 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-12 * G.3^4 * G.2^-12 * G.3 ] Genus 70 action of group of order 282 via triangle group [ 2, 141, 282 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^116 * G.3^-24 * G.2 ] Genus 70 action of group of order 284 via triangle group [ 2, 142, 142 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^25 * G.2^-115 * G.3 ] Genus 70 action of group of order 280 via triangle group [ 2, 280, 280 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^24 * G.2^-114 * G.3 ] Genus 70 action of group of order 360 via triangle group [ 3, 4, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.1 * G.3^-4, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 70 action of group of order 360 via triangle group [ 3, 5, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-5, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 70 action of group of order 284 via triangle group [ 4, 4, 71 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-71 ] Genus 70 action of group of order 280 via triangle group [ 4, 4, 140 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-55 * G.1 * G.2^-1 * G.3^-14 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 ] Genus 70 action of group of order 552 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 70 action of group of order 284 via quadrangle group [ 2, 2, 2, 71 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-35 * G.2 * G.1 * G.3 * G.4^-35 ] Genus 70 action of group of order 284 via quadrangle group [ 2, 2, 2, 71 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-64 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 70 action of group of order 284 via quadrangle group [ 2, 2, 2, 71 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^53 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 70 action of group of order 280 via quadrangle group [ 2, 2, 2, 140 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-35 * G.1 * G.4^-35 ] Genus 70 action of group of order 280 via quadrangle group [ 2, 2, 2, 140 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-63 * G.1 * G.3 * G.4^-6 ] Genus 70 action of group of order 280 via quadrangle group [ 2, 2, 2, 140 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^43 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Largest orientation-preserving group for genus 70 has order 660 ... group action with signature (0: +; [2,5,11]; {-}) Largest group with or without reflections for genus 70 has order 1320 ... group action with signature (0; +; [-]; {(2,5,11)}) Largest group with reflections for genus 70 has order 1320 ... group action with signature (0; +; [-]; {(2,5,11)}) Largest chiral group for genus 70 has order 552 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 71 has order 552 ... group action with signature (0; +; [2]; {(2,4)}) Check total 125 : 90 chiral, 35 reflexible, with 6 non-orientable quotient actions Genus 71 actions: Genus 71 action of group of order 640 via triangle group [ 2, 4, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.3^5 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 ] Genus 71 action of group of order 640 via triangle group [ 2, 4, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-10 * G.1 * G.3^9 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 71 action of group of order 640 via triangle group [ 2, 4, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.3 ] Genus 71 action of group of order 640 via triangle group [ 2, 4, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-9 * G.1 * G.3^11 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 600 via triangle group [ 2, 4, 60 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-5 * G.1 * G.3^13 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 71 action of group of order 600 via triangle group [ 2, 4, 60 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-9 * G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 576 via triangle group [ 2, 4, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-57 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 71 action of group of order 576 via triangle group [ 2, 4, 144 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-144 ] Genus 71 action of group of order 568 via triangle group [ 2, 4, 284 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-30 * G.1 * G.2^-1 * G.3^-111 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^8, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, (G.2^-2 * G.3)^3 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 71 action of group of order 672 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 71 action of group of order 462 via triangle group [ 2, 6, 33 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 462 via triangle group [ 2, 6, 33 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 426 via triangle group [ 2, 6, 213 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^57 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^3 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-12 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-12 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-12 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-12 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 71 action of group of order 480 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-4, G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.1 * G.2^-1 ] Genus 71 action of group of order 400 via triangle group [ 2, 8, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 71 action of group of order 400 via triangle group [ 2, 8, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 71 action of group of order 400 via triangle group [ 2, 8, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 71 action of group of order 400 via triangle group [ 2, 8, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^4 ] Genus 71 action of group of order 384 via triangle group [ 2, 8, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^35 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 71 action of group of order 384 via triangle group [ 2, 8, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-17 * G.1 * G.3^16 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-11 ] Genus 71 action of group of order 504 via triangle group [ 2, 9, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.1 * G.3^2 ] Genus 71 action of group of order 504 via triangle group [ 2, 9, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-3 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-4, G.3^-2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 320 via triangle group [ 2, 20, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-6 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 71 action of group of order 320 via triangle group [ 2, 20, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2^-1 * G.3^4 * G.2^-11 * G.3^3 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^5 * G.2^-1 * G.3 * G.2^-12 * G.3^3 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^2 * G.2^-1 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-9 * G.3^3 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-11 * G.3 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.3^-1 * G.2^6 * G.3^-5 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-14 ] Genus 71 action of group of order 336 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2^6 * G.3^-5 ] Genus 71 action of group of order 320 via triangle group [ 2, 32, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-12 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 71 action of group of order 320 via triangle group [ 2, 32, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-7 * G.3^2 * G.2^-1 ] Genus 71 action of group of order 320 via triangle group [ 2, 32, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^11 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-10 * G.3^3 ] Genus 71 action of group of order 320 via triangle group [ 2, 32, 32 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-6 * G.3 * G.2^-2 ] Genus 71 action of group of order 300 via triangle group [ 2, 60, 60 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-10 * G.3 * G.2^-1 * G.3^4 * G.2^-11 * G.3 * G.2^-1 * G.3 ] Genus 71 action of group of order 300 via triangle group [ 2, 60, 60 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^9 * G.2^-4 * G.3^2 * G.2^-10 * G.3 * G.2^-1 * G.3^3 ] Genus 71 action of group of order 286 via triangle group [ 2, 143, 286 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^117 * G.3^-26 ] Genus 71 action of group of order 288 via triangle group [ 2, 144, 144 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^26 * G.2^-117 ] Genus 71 action of group of order 288 via triangle group [ 2, 144, 144 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-41 * G.2^12 * G.3^-1 * G.2^18 ] Genus 71 action of group of order 284 via triangle group [ 2, 284, 284 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^25 * G.2^-116 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^8, (G.2 * G.3^-1)^4 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.1^-1 * G.2^-3 * G.1 * G.2^-2 * G.3, G.2^8 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.3^-1 * G.2)^2, G.2^8 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.2^8 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^2, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^8, G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.2^3 * G.3^-1 * G.2^2 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^8, (G.1^-1 * G.3 * G.2^2)^2, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^3 * G.1^-1 * G.3^3, G.2^8 ] Genus 71 action of group of order 336 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3, G.2^3 * G.1^-1 * G.3^3 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-3 * G.1^-1 * G.3^4, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-6 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-4 ] Genus 71 action of group of order 320 via triangle group [ 4, 4, 16 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-6 * G.1^-1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^-8 ] Genus 71 action of group of order 300 via triangle group [ 4, 4, 30 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-5 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 71 action of group of order 300 via triangle group [ 4, 4, 30 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-5 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-72 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-23 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-24 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^29 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-23 * G.1 * G.3^6 * G.2^-1 * G.3^-6 ] Genus 71 action of group of order 288 via triangle group [ 4, 4, 72 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^28 * G.2^-1 * G.3^-7 * G.1 ] Genus 71 action of group of order 284 via triangle group [ 4, 4, 142 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-56 * G.1 * G.2^-1 * G.3^-14 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^6, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^6, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.2^-1)^4 ] Genus 71 action of group of order 336 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.3 * G.1^-1 * G.2^-1)^2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 560 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3)^2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 420 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^7 * G.1^2 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-7 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^7 * G.1^2 * G.4^5, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-5 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-12, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.4^2 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.1 * G.4^2 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-4 * G.1 * G.4^2 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-4 * G.1 * G.4^2 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-7 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^7 * G.1^2 * G.4^5, (G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.3 * G.1 * G.3 * G.4^-5 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^5 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^5 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^5 * G.3 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^5 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^7 * G.1^2 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-12, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-5 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.3 * G.1 * G.3 * G.4^-5 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^5 * G.3 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.2 * G.4^4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-9 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^6 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-7 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-9 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-16 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-6 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^6 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4^5 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^11 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-11 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-8 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4, G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^8 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.3 * G.4^-6 * G.1 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^7 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^7 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^5 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.2 * G.4^4, G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4, G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^6 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-5 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^11 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.3 * G.4^-10 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-5 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 71 action of group of order 320 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.1 * G.4^-1 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-6 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^5 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.4^7 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-5 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 71 action of group of order 308 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^5, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^6 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^4 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-7 * G.2 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.4^-5 * G.1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^9 * G.3 * G.4^-5 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^7 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.1 * G.4^-1 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-8 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^9 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.2 * G.4^-6 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^3 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^2 * G.3 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-6 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 71 action of group of order 300 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-72 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-72 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^54 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-7 * G.2 * G.4^2 * G.3 * G.4^-14 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^8 * G.3 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^29 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^10 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^15 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-13 * G.2 * G.4^11 * G.1 * G.3 * G.4^-11 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-18 * G.1 * G.4^-5 * G.1 * G.4^-13 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-16 * G.2 * G.4^-5 * G.1 * G.2 * G.4^5 * G.2 * G.4^3 * G.3 * G.4^-6 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-14 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^7 * G.2 * G.4^-8 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^21 * G.1 * G.4^-9 * G.1 * G.4^6 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^13 * G.2 * G.4^-11 * G.1 * G.2 * G.1 * G.4^10 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-9 * G.1 * G.4^-5 * G.1 * G.4^-4 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-7 * G.1 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-3 * G.1 * G.3 * G.4^-7 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^7 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^6 * G.3 * G.1 * G.2 * G.4^5 * G.2 * G.4^4 * G.2 * G.4^2 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4^2 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-11 * G.2 * G.1 * G.4^2 * G.3 * G.4^-4 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-3 * G.1 * G.4^6 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^4 * G.2 * G.4^-5 * G.1 * G.4^2 * G.1^2 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7 * G.2 * G.1 * G.4^2 * G.3 * G.4^-8 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-6 * G.1 * G.2 * G.1 * G.4^8 * G.2 * G.4^-2 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-9 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-6 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-3 * G.1 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-6 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^6 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^2 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-2 * G.1 * G.4^-10 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^9 * G.3 * G.4^-2 * G.2 * G.3 * G.2 * G.4^5 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^4 * G.3 * G.4^-2 * G.1 * G.4^10 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7 * G.2 * G.1 * G.3 * G.4^-10 ] Genus 71 action of group of order 288 via quadrangle group [ 2, 2, 2, 72 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-6 * G.1 * G.4^4 * G.2 * G.4^-2 * G.1 * G.4^4 * G.2 ] Genus 71 action of group of order 284 via quadrangle group [ 2, 2, 2, 142 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-35 * G.2 * G.3 * G.4^-35 ] Genus 71 action of group of order 284 via quadrangle group [ 2, 2, 2, 142 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-64 * G.2 * G.4^-7 ] Genus 71 action of group of order 284 via quadrangle group [ 2, 2, 2, 142 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^44 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.4 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.2 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.2 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.3)^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.4^-1 * G.3)^3, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.3 * G.4^-1)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.3 * G.4^-1)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.3 * G.4^-1)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3, (G.3^-1 * G.1)^3, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, (G.1 * G.2)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.3^-1 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.4^-1 * G.3)^3, (G.1 * G.2)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.2 * G.3 * G.1 * G.2 * G.4^2, (G.4^-1 * G.2)^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2^-1 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.3)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.2 * G.3 * G.1 * G.2 * G.4^2, (G.4^-1 * G.2^-1)^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.4^-1)^4, G.3 * G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4, G.2 * G.4^-2 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^2 * G.2, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^2 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-2 * G.2^-1 * G.3 * G.2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.2 * G.4^-2 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.4^-1)^4, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.1 * G.2^-1 * G.4^2, G.4 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4^2 * G.2^-1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 71 action of group of order 336 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 ] Largest orientation-preserving group for genus 71 has order 672 ... group action with signature (0: +; [2,6,8]; {-}) Largest group with or without reflections for genus 71 has order 1344 ... group action with signature (0; +; [-]; {(2,6,8)}) Largest group with reflections for genus 71 has order 1344 ... group action with signature (0; +; [-]; {(2,6,8)}) Largest chiral group for genus 71 has order 640 ... group action with signature (0: +; [2,4,32]; {-}) Largest non-orientable group for non-orientable genus 72 has order 672 ... group action with signature (0; +; [-]; {(2,6,8)}) Check total 812 : 582 chiral, 230 reflexible, with 106 non-orientable quotient actions Genus 72 actions: Genus 72 action of group of order 600 via triangle group [ 2, 4, 75 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-58 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 72 action of group of order 584 via triangle group [ 2, 4, 146 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-146 ] Genus 72 action of group of order 576 via triangle group [ 2, 4, 288 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-31 * G.1 * G.2^-1 * G.3^-112 ] Genus 72 action of group of order 710 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-4 * G.2 ] Genus 72 action of group of order 710 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^4 * G.2^-1 ] Genus 72 action of group of order 710 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 ] Genus 72 action of group of order 710 via triangle group [ 2, 5, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 72 action of group of order 444 via triangle group [ 2, 6, 74 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^54 * G.2^-1 * G.1 * G.3^19 ] Genus 72 action of group of order 400 via triangle group [ 2, 8, 50 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-26 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-11 ] Genus 72 action of group of order 380 via triangle group [ 2, 10, 38 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-7 * G.1 * G.3^16 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-5 ] Genus 72 action of group of order 360 via triangle group [ 2, 10, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-6 * G.1 * G.3^16 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 72 action of group of order 364 via triangle group [ 2, 14, 26 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^8 * G.2 * G.1 * G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^8 ] Genus 72 action of group of order 336 via triangle group [ 2, 14, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^7 * G.3^-3, G.2 * G.1 * G.3^11 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-5 * G.1 * G.3 ] Genus 72 action of group of order 360 via triangle group [ 2, 18, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^10, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 72 action of group of order 320 via triangle group [ 2, 20, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.3^-2 * G.1 * G.3^5 ] Genus 72 action of group of order 336 via triangle group [ 2, 24, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^5 * G.2^5 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 72 action of group of order 312 via triangle group [ 2, 26, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-12 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 72 action of group of order 306 via triangle group [ 2, 34, 153 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-2 * G.3^4 * G.2^-6 * G.3^3 ] Genus 72 action of group of order 304 via triangle group [ 2, 38, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2^7 * G.3^-4 * G.2^17 * G.3^-1 ] Genus 72 action of group of order 312 via triangle group [ 2, 39, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-9 * G.3^4 ] Genus 72 action of group of order 300 via triangle group [ 2, 50, 150 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-18 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^18 ] Genus 72 action of group of order 296 via triangle group [ 2, 74, 148 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.3^-39 * G.2 * G.3^-2 * G.2^30 ] Genus 72 action of group of order 300 via triangle group [ 2, 75, 75 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-71 * G.3 * G.2^-1 ] Genus 72 action of group of order 294 via triangle group [ 2, 98, 147 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-17 * G.2 * G.3^-2 * G.2^10 * G.3^-2 * G.2^15 * G.3^-2 ] Genus 72 action of group of order 290 via triangle group [ 2, 145, 290 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^118 * G.3^-26 * G.2 ] Genus 72 action of group of order 292 via triangle group [ 2, 146, 146 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^27 * G.2^-117 * G.3 ] Genus 72 action of group of order 288 via triangle group [ 2, 288, 288 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^26 * G.2^-116 * G.3 ] Genus 72 action of group of order 444 via triangle group [ 3, 3, 74 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 72 action of group of order 444 via triangle group [ 3, 3, 74 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2 * G.3^-6 * G.1^-1 ] Genus 72 action of group of order 292 via triangle group [ 4, 4, 73 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-64 * G.1^-1 * G.2^-1 * G.3^-8 ] Genus 72 action of group of order 292 via triangle group [ 4, 4, 73 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6 * G.1^-1 * G.3^2 * G.2^-1 * G.3^2 ] Genus 72 action of group of order 292 via triangle group [ 4, 4, 73 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.1^-1 * G.3^7 * G.2^-1 ] Genus 72 action of group of order 288 via triangle group [ 4, 4, 144 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-57 * G.1 * G.2^-1 * G.3^-14 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2^-2 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.2^-1 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3^2 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3 ] Genus 72 action of group of order 355 via triangle group [ 5, 5, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.2^-2 ] Genus 72 action of group of order 292 via quadrangle group [ 2, 2, 2, 73 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-36 * G.2 * G.1 * G.3 * G.4^-36 ] Genus 72 action of group of order 292 via quadrangle group [ 2, 2, 2, 73 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-66 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 72 action of group of order 292 via quadrangle group [ 2, 2, 2, 73 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^55 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 72 action of group of order 288 via quadrangle group [ 2, 2, 2, 144 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-36 * G.1 * G.4^-36 ] Genus 72 action of group of order 288 via quadrangle group [ 2, 2, 2, 144 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-65 * G.1 * G.3 * G.4^-6 ] Genus 72 action of group of order 288 via quadrangle group [ 2, 2, 2, 144 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^45 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Largest orientation-preserving group for genus 72 has order 710 ... group action with signature (0: +; [2,5,10]; {-}) Largest group with or without reflections for genus 72 has order 1200 ... group action with signature (0; +; [-]; {(2,4,75)}) Largest group with reflections for genus 72 has order 1200 ... group action with signature (0; +; [-]; {(2,4,75)}) Largest chiral group for genus 72 has order 710 ... group action with signature (0: +; [2,5,10]; {-}) Largest non-orientable group for non-orientable genus 73 has order 600 ... group action with signature (0; +; [-]; {(2,4,75)}) Check total 51 : 16 chiral, 35 reflexible, with 11 non-orientable quotient actions Genus 73 actions: Genus 73 action of group of order 2160 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 73 action of group of order 2160 via triangle group [ 2, 3, 10 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 ] Genus 73 action of group of order 2160 via triangle group [ 2, 3, 10 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 2160 via triangle group [ 2, 3, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 1728 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 1728 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 73 action of group of order 1152 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 1152 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 73 action of group of order 1080 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-3 * G.1 * G.3, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 1008 via triangle group [ 2, 3, 42 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 1728 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 1344 via triangle group [ 2, 4, 7 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 1344 via triangle group [ 2, 4, 7 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^6, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-3 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^8 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.2 * G.3^-2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^3 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 73 action of group of order 1152 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 73 action of group of order 960 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^10, (G.2 * G.3^-1)^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3 ] Genus 73 action of group of order 864 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 864 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 73 action of group of order 864 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3^12 ] Genus 73 action of group of order 864 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^12, G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 864 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4, G.3^12, G.3^-3 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 720 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2 * G.3^-1)^6, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 73 action of group of order 672 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 672 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-4 * G.2 * G.3^-4 * G.1 ] Genus 73 action of group of order 648 via triangle group [ 2, 4, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2 * G.3^-1)^6, G.3^7 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 ] Genus 73 action of group of order 640 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-21 * G.1 * G.3^11 * G.2^-1 * G.3^-7 ] Genus 73 action of group of order 640 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 73 action of group of order 640 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^4 * G.2 * G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 * G.1 ] Genus 73 action of group of order 640 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^6 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 608 via triangle group [ 2, 4, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-60 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 73 action of group of order 592 via triangle group [ 2, 4, 148 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-148 ] Genus 73 action of group of order 584 via triangle group [ 2, 4, 292 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-32 * G.1 * G.2^-1 * G.3^-113 ] Genus 73 action of group of order 720 via triangle group [ 2, 5, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1, G.3^10, G.3 * G.2 * G.3^-3 * G.2^2 * G.3^-3 * G.1 * G.2^-1 ] Genus 73 action of group of order 720 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2 ] Genus 73 action of group of order 864 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.1 ] Genus 73 action of group of order 864 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3 * G.2^-1 * G.3)^3, (G.2 * G.3^-1 * G.2)^4 ] Genus 73 action of group of order 864 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 864 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2^-2 * G.3)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 73 action of group of order 864 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-4 * G.1 * G.2 * G.3^-4 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 648 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^12 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^12 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-3 * G.2^2 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3^-3 * G.1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2^-2 * G.3)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 73 action of group of order 576 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-12 ] Genus 73 action of group of order 504 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-11 ] Genus 73 action of group of order 486 via triangle group [ 2, 6, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^8 * G.2 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 486 via triangle group [ 2, 6, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 73 action of group of order 486 via triangle group [ 2, 6, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 73 action of group of order 480 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 73 action of group of order 456 via triangle group [ 2, 6, 57 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 450 via triangle group [ 2, 6, 75 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-41 * G.1 * G.3^18 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 73 action of group of order 438 via triangle group [ 2, 6, 219 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-40 * G.1 * G.3^17 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^-3 * G.3^-4 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 480 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^10, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2, G.3^10, G.2^-1 * G.3 * G.2^-4 * G.3^-1 * G.2^2 * G.3^-1 * G.1 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, (G.2 * G.3^-1)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.2^2 * G.1 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2, (G.2^-1 * G.3)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-2 * G.2)^2, G.3 * G.2^5 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2^-1 * G.3)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^12, (G.2^-1 * G.3)^6 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.3^-12 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 432 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-5 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.2^12, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^12 ] Genus 73 action of group of order 384 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2, G.2^12 ] Genus 73 action of group of order 360 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.1 * G.3^12 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 73 action of group of order 360 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-13 * G.1 * G.3 ] Genus 73 action of group of order 360 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 73 action of group of order 360 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 73 action of group of order 360 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 360 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-12 * G.3 * G.2^-1 * G.3^3 ] Genus 73 action of group of order 336 via triangle group [ 2, 21, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-8 * G.3 * G.2^-2 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 2, 21, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-3 * G.3 * G.2^-2 * G.3^4 * G.2^-7 * G.3 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 324 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 73 action of group of order 324 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 324 via triangle group [ 2, 36, 36 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-2 * G.3^2 * G.2^-9 * G.3 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 73 action of group of order 312 via triangle group [ 2, 39, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-39 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-5 * G.2 * G.3^-1 * G.2^10 * G.3^-4 * G.2^18 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-23 * G.3^3 * G.2^-10 * G.3^2 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2 * G.3^-6 * G.2 * G.3^-1 * G.2^11 * G.3^-3 * G.2 * G.3^-16 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^6 * G.2^-11 * G.3^2 * G.2^-1 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-2 * G.3^3 * G.2^-11 * G.3 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 320 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^3 * G.2^-1 * G.3^3 * G.2^-10 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 306 via triangle group [ 2, 51, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-20 * G.2^10 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-15 * G.2 ] Genus 73 action of group of order 304 via triangle group [ 2, 76, 76 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-43 * G.2^2 * G.3^-1 * G.2^30 ] Genus 73 action of group of order 294 via triangle group [ 2, 147, 294 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^106 * G.2^-40 ] Genus 73 action of group of order 296 via triangle group [ 2, 148, 148 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^41 * G.3^-106 * G.2 ] Genus 73 action of group of order 292 via triangle group [ 2, 292, 292 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^27 * G.2^-118 ] Genus 73 action of group of order 1080 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^2 * G.2 * G.3^-1)^2 ] Genus 73 action of group of order 1080 via triangle group [ 3, 3, 5 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 ] Genus 73 action of group of order 1080 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 73 action of group of order 1080 via triangle group [ 3, 3, 5 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1 * G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1^-1 * G.3 * G.2 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 864 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, (G.1 * G.3^2 * G.2 * G.3^-1)^2 ] Genus 73 action of group of order 576 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 73 action of group of order 540 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1^-1 * G.3^2 * G.2)^2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1 * G.3^2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 504 via triangle group [ 3, 3, 21 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 ] Genus 73 action of group of order 468 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 73 action of group of order 468 via triangle group [ 3, 3, 39 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 73 action of group of order 441 via triangle group [ 3, 3, 147 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2 * G.3^-1 * G.1^-2 * G.3^5 ] Genus 73 action of group of order 441 via triangle group [ 3, 3, 147 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^8 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 ] Genus 73 action of group of order 864 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, (G.1 * G.3^2 * G.2^-1 * G.3^-1)^2 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, (G.1^-1 * G.3^2 * G.2)^2, (G.1 * G.3^2 * G.2 * G.3^-1)^2 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 73 action of group of order 432 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 73 action of group of order 432 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^12 ] Genus 73 action of group of order 432 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-4 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 384 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 ] Genus 73 action of group of order 360 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-2 * G.2^2 * G.1^-1 * G.3 * G.2^3 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^8 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3^2 * G.2^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3^-1 * G.1 * G.2^-2 * G.1 * G.2^-2 * G.3^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^8, G.2 * G.3^-3 * G.1^-1 * G.2 * G.3^-3 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.2^6, G.1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2 ] Genus 73 action of group of order 384 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3, G.1 * G.3 * G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 73 action of group of order 360 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3 * G.2^2 * G.1^-1 * G.3^3, (G.1 * G.3^2 * G.2)^2 ] Genus 73 action of group of order 360 via triangle group [ 3, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, (G.1 * G.3 * G.2^2)^2 ] Genus 73 action of group of order 360 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, (G.1^-1 * G.3^2 * G.2^-1 * G.3^-1)^2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^2 * G.2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 336 via triangle group [ 3, 6, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 73 action of group of order 312 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 312 via triangle group [ 3, 6, 26 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 73 action of group of order 294 via triangle group [ 3, 6, 98 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.2^-1 * G.3^-3 * G.1^-1 * G.3^4 ] Genus 73 action of group of order 294 via triangle group [ 3, 6, 98 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-4 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-9, G.3^2 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-2 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, (G.1 * G.3 * G.2)^2, G.3^4 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 324 via triangle group [ 3, 9, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^3 * G.3^-2, G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, (G.1 * G.2^-1)^4, (G.2 * G.1^-1 * G.3)^3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, (G.1^-1 * G.2^-1 * G.1 * G.3)^3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, (G.1 * G.2^-1)^4, (G.3^-1 * G.1^-1 * G.2)^3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, (G.1 * G.3^-1)^4, (G.3 * G.1^-1 * G.2^-1)^3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1^-1 * G.2)^6 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.3 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.1^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 73 action of group of order 576 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 73 action of group of order 480 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^6, (G.1 * G.2^-1)^6 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, (G.1 * G.2^-1)^6 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1^2 * G.3^2 * G.1^-1 * G.3 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.3^2 * G.2)^2 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 73 action of group of order 432 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 73 action of group of order 360 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1, G.3^10 ] Genus 73 action of group of order 360 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 73 action of group of order 360 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 73 action of group of order 336 via triangle group [ 4, 4, 14 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2, (G.1 * G.3^-2 * G.2)^2 ] Genus 73 action of group of order 336 via triangle group [ 4, 4, 14 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1 * G.3^-1 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 324 via triangle group [ 4, 4, 18 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-6 * G.1^-1 * G.3^4 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^-8 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^9 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-6 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^5 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3^5 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^5 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^5 * G.2 * G.3^-5 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^8 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^13 * G.2^-1 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-6 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^13 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-10 * G.1 * G.3^8 * G.2 * G.3^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^8 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^-3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.1 * G.3^-8 * G.2 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1^2 * G.3^4 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-6 * G.1 * G.3^-3 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.2 * G.1^2 * G.3 * G.2 * G.3^-2 ] Genus 73 action of group of order 320 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 304 via triangle group [ 4, 4, 38 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-24 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-6 ] Genus 73 action of group of order 296 via triangle group [ 4, 4, 74 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^58 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 73 action of group of order 296 via triangle group [ 4, 4, 74 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6 * G.2 * G.3^-4 * G.1 * G.3 ] Genus 73 action of group of order 296 via triangle group [ 4, 4, 74 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.2 * G.3^-3 * G.1^2 * G.3 * G.2 * G.3^-4 ] Genus 73 action of group of order 292 via triangle group [ 4, 4, 146 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-64 * G.1^-1 * G.2 * G.3^-8 ] Genus 73 action of group of order 320 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 73 action of group of order 320 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^2 * G.2^-1 * G.1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 73 action of group of order 320 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 320 via triangle group [ 4, 5, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-5, G.3^-3 * G.2 * G.1 * G.3 * G.2^2 ] Genus 73 action of group of order 360 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, (G.1 * G.2^-2)^2, G.2^-5, (G.1 * G.3 * G.2^-1)^2 ] Genus 73 action of group of order 360 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.2^-2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2^-1 * G.1^2 * G.3^2 * G.1^-1 ] Genus 73 action of group of order 360 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2 ] Genus 73 action of group of order 360 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.1^-1 * G.2^-1 * G.1^2 * G.3 * G.1^-1, G.2^-5, (G.1^-1 * G.3 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 864 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^18 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^36 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^18 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^18 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^36 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^18 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, (G.3 * G.1)^9 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^24 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^9 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^36 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^18 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.4^-2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^-2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1 * G.1 * G.4)^4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, (G.1 * G.2)^8 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^8 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.4^-2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^12 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.4^-1 * G.2)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.3 * G.1)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 576 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^6, G.4 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.1 * G.4^-2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.4^2 ] Genus 73 action of group of order 480 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^36 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^9 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^12 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, (G.1 * G.3)^12 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^18 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^18 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^18 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2)^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^12 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, (G.3 * G.1)^9 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.3 * G.1)^9 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.3 * G.1 * G.3 * G.1 * G.4)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.3 * G.1)^9 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.2 * G.4^2 * G.2 * G.4^-2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.4 * G.3 * G.4^-1 * G.1)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.2)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.2)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.4^2 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^12 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.2 * G.4^-1)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.1 * G.2)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4^-1)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^8, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^8, G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^8, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.4^3 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^8, (G.1 * G.4^3 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.4^-1 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4^4 * G.1^2 * G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^8, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^12 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 384 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, (G.1 * G.3)^6 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3)^6 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, (G.1 * G.3)^6 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, (G.1 * G.3)^6 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.4^-1 * G.2)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.4^-1 * G.2)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.3 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^10, G.1 * G.3 * G.4^-2 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^10, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, (G.3 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^5, (G.2 * G.4^2 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3, (G.3 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^10, G.4^3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, (G.4^-1 * G.2)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.3 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.2 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.2 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.1)^5 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^10, G.3 * G.2 * G.4^3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^10, G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^2 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 360 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^9 * G.1^2 * G.4^5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-9 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-14 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.3 * G.1 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^14, (G.1 * G.3)^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^7 * G.1^2 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.4 * G.2 * G.4^-3 * G.1 * G.4^2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.4 * G.2 * G.4^-3 * G.1 * G.4^2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2, (G.1 * G.3)^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^7 * G.3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.3 * G.1 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^-9 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^9 * G.1^2 * G.4^5, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^8 * G.1^2 * G.4^6 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^5 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.1 * G.4)^3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1 * G.4)^3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 73 action of group of order 336 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^13 * G.1^2 * G.4^5, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6, G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^4 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, (G.1 * G.3)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-3, (G.1 * G.2)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4^4 * G.3 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4 * G.3 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.4^-4 * G.2 * G.4^4, (G.1 * G.2)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.3 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^4 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2, G.4^6 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4, G.3 * G.2 * G.4^4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^6 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-4 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, (G.1 * G.2)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^5 * G.2 * G.1 * G.4^4 * G.2 * G.4^2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.1 * G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.4 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^5 * G.3 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-4 * G.1 * G.4 * G.2 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, (G.1 * G.2)^6 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 324 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-20 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-7 * G.2 * G.4^2 * G.1 * G.3 * G.4^-10 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-14 * G.1^2 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^7 * G.3 * G.4^-3 * G.1^2 * G.4^-5 * G.2 * G.4^3 * G.3 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 * G.4^9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-8 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-5 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6 * G.2 * G.4^-6 * G.1 * G.4^2 * G.1^2 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-7 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^7 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-4 * G.1 * G.2 * G.3 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-20 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^9 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.2 * G.4^4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^8 * G.1 * G.4 * G.1^2 * G.3 * G.4^-10 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-7 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^9 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-5 * G.1 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.4^-6 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.4^-3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^10 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.2 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-5 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4 * G.2 * G.4^-7 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^-2 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-20 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-8 * G.1 * G.3 * G.1^2 * G.4^-3 * G.1 * G.3 * G.4^-7 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-3 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^10 * G.3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-2 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.4^9 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4^2 * G.1 * G.3 * G.4^-10 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-8 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^10 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^6 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4^8 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^11 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^7 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.3 * G.4^-8 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^9 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-5 * G.1 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4^3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-13 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-20 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^14 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 73 action of group of order 320 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-7 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^7 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^6 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.3 * G.4^-7 * G.2 * G.1 * G.4 * G.2 * G.4^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^7 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^-7 * G.1 * G.3 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.3 * G.4^-9 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.1 * G.4 * G.2 * G.1^2 * G.4^-6 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-8 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^14 * G.3 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^10 * G.3 * G.4^-1 * G.1 * G.4^-13 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^21 * G.1^2 * G.4^5 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-26 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^26 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^26 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^20 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^9 * G.3 * G.1 * G.4 * G.3 * G.4^-6 * G.1 * G.4^8 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-16 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-7 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-10 * G.1 * G.4 * G.2 * G.1 * G.4^11 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-12 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 73 action of group of order 312 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.4 * G.2 * G.4^-7 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^13 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-11 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^8 * G.1^2 * G.4 * G.3 * G.4^-8 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^8 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.4^-5 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-12 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^12 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^2 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^12 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^12 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-12 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^4 * G.2 * G.4^-5 * G.1 * G.3 * G.2 * G.1 * G.4^8 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-38 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-14 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-12 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^21 * G.3 * G.1 * G.3 * G.1^2 * G.4^-9 * G.1 * G.4^6 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^16 * G.3 * G.4^-6 * G.1 * G.4 * G.2 * G.4^14 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^14 * G.2 * G.4^-10 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-16 * G.1 * G.4^4 * G.2 * G.1 * G.4^11 * G.2 * G.4^-5 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-11 * G.2 * G.4 * G.3 * G.4^-13 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-6 * G.2 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-33 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 304 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-14 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-12 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-11 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^13 * G.1^2 * G.3 * G.4^-11 * G.2 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-14 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^15 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-18 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^19 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4 * G.3 * G.4^-8 * G.1 * G.2 * G.4 * G.2 * G.4^14 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^8 * G.3 * G.1 * G.4 * G.1 * G.4^-9 * G.1 * G.4^6 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^13 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-11 * G.1 * G.4^6 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^12 * G.2 * G.4^-2 ] Genus 73 action of group of order 300 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-9 * G.1 * G.4^13 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-11 * G.2 * G.4^16 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^6 * G.3 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-9 * G.2 * G.4^16 * G.3 * G.4^-1 * G.2 * G.4^6 * G.3 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-32 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^31 * G.3 * G.1 * G.4^5 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^12 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.1^2 * G.2 * G.4^-12 * G.1 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-74 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-74 ] Genus 73 action of group of order 296 via quadrangle group [ 2, 2, 2, 74 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^60 * G.2 * G.1 * G.2 * G.1 * G.4^12 ] Genus 73 action of group of order 292 via quadrangle group [ 2, 2, 2, 146 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-36 * G.2 * G.3 * G.4^-36 ] Genus 73 action of group of order 292 via quadrangle group [ 2, 2, 2, 146 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-66 * G.2 * G.4^-7 ] Genus 73 action of group of order 292 via quadrangle group [ 2, 2, 2, 146 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^46 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^16 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^8, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^8, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1^2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, (G.2 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.3^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^4, G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.3 * G.4^-1)^4, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.3 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3, (G.2 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.1 * G.2^-1 * G.3)^3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^4, (G.1 * G.3)^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.2^-1 * G.3 * G.1)^4, (G.1 * G.3)^6, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1)^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1)^4, (G.2^-1 * G.4^-1)^6, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4, G.3 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2 * G.4^-1)^4, (G.2^-1 * G.4^-1)^6, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.4 * G.3 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.4 * G.3 * G.1)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 73 action of group of order 432 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.3 ] Largest orientation-preserving group for genus 73 has order 2160 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 73 has order 4320 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 73 has order 4320 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 73 has order 2160 ... group action with signature (0: +; [2,3,10]; {-}) Largest non-orientable group for non-orientable genus 74 has order 2160 ... group action with signature (0; +; [-]; {(2,3,10)}) Check total 4499 : 2772 chiral, 1727 reflexible, with 296 non-orientable quotient actions Genus 74 actions: Genus 74 action of group of order 600 via triangle group [ 2, 4, 150 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-30 * G.1 * G.2 * G.3^-119 ] Genus 74 action of group of order 592 via triangle group [ 2, 4, 296 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-35 * G.1 * G.2^-1 * G.3^-112 ] Genus 74 action of group of order 876 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 74 action of group of order 876 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 74 action of group of order 876 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 74 action of group of order 876 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 74 action of group of order 456 via triangle group [ 2, 6, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-42 * G.1 * G.3^12 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-19 ] Genus 74 action of group of order 444 via triangle group [ 2, 6, 222 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-38 * G.1 * G.3 * G.2 * G.1 * G.3^18 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 74 action of group of order 584 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 74 action of group of order 584 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 ] Genus 74 action of group of order 584 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 74 action of group of order 584 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 74 action of group of order 432 via triangle group [ 2, 8, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 ] Genus 74 action of group of order 400 via triangle group [ 2, 8, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-26 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-17 ] Genus 74 action of group of order 370 via triangle group [ 2, 10, 185 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-6 * G.1 * G.3^22 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 74 action of group of order 352 via triangle group [ 2, 16, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-5 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-6 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^4 ] Genus 74 action of group of order 336 via triangle group [ 2, 21, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 74 action of group of order 336 via triangle group [ 2, 24, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-4 * G.2 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 74 action of group of order 312 via triangle group [ 2, 52, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-12 * G.3^4 * G.2^-6 * G.3^2 * G.2^-2 ] Genus 74 action of group of order 304 via triangle group [ 2, 76, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2^7 * G.3^-4 * G.2^18 ] Genus 74 action of group of order 298 via triangle group [ 2, 149, 298 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^107 * G.2^-40 * G.3 ] Genus 74 action of group of order 300 via triangle group [ 2, 150, 150 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^42 * G.3^-108 ] Genus 74 action of group of order 296 via triangle group [ 2, 296, 296 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^41 * G.3^-107 ] Genus 74 action of group of order 456 via triangle group [ 3, 3, 76 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.1^-1 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 74 action of group of order 456 via triangle group [ 3, 3, 76 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-4 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 74 action of group of order 438 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 74 action of group of order 438 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 74 action of group of order 438 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 ] Genus 74 action of group of order 438 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 74 action of group of order 300 via triangle group [ 4, 4, 75 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.2 * G.3^-1 ] Genus 74 action of group of order 300 via triangle group [ 4, 4, 75 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^59 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 74 action of group of order 300 via triangle group [ 4, 4, 75 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^2 ] Genus 74 action of group of order 296 via triangle group [ 4, 4, 148 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^58 * G.2^-1 * G.1 * G.3^15 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-12 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-11 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-6 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-12 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^7 * G.2 * G.4^-4 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.4^6 * G.2 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-7 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^6 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-37 * G.2 * G.1 * G.3 * G.4^-37 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-68 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 74 action of group of order 300 via quadrangle group [ 2, 2, 2, 75 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-75 ] Genus 74 action of group of order 296 via quadrangle group [ 2, 2, 2, 148 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-37 * G.1 * G.4^-37 ] Genus 74 action of group of order 296 via quadrangle group [ 2, 2, 2, 148 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-67 * G.1 * G.3 * G.4^-6 ] Genus 74 action of group of order 296 via quadrangle group [ 2, 2, 2, 148 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^60 * G.2 * G.1 * G.4^13 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.1^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.3 * G.1 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.3 * G.1 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.2 * G.1, G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 74 action of group of order 438 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Largest orientation-preserving group for genus 74 has order 876 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 74 has order 1200 ... group action with signature (0; +; [-]; {(2,4,150)}) Largest group with reflections for genus 74 has order 1200 ... group action with signature (0; +; [-]; {(2,4,150)}) Largest chiral group for genus 74 has order 876 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 75 has order 438 ... group action with signature (0; +; [2,3]; {(1)}) Check total 341 : 300 chiral, 41 reflexible, with 8 non-orientable quotient actions Genus 75 actions: Genus 75 action of group of order 1776 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 1776 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 1184 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 75 action of group of order 1184 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 75 action of group of order 1184 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 75 action of group of order 1184 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 75 action of group of order 888 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 75 action of group of order 888 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 75 action of group of order 624 via triangle group [ 2, 4, 78 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-61 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 75 action of group of order 608 via triangle group [ 2, 4, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-68 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 75 action of group of order 608 via triangle group [ 2, 4, 152 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-31 * G.1 * G.2 * G.3^-120 ] Genus 75 action of group of order 600 via triangle group [ 2, 4, 300 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-30 * G.1 * G.2^-1 * G.3^-119 ] Genus 75 action of group of order 480 via triangle group [ 2, 6, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 75 action of group of order 480 via triangle group [ 2, 6, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 75 action of group of order 592 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 75 action of group of order 592 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 75 action of group of order 592 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 75 action of group of order 480 via triangle group [ 2, 8, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 75 action of group of order 416 via triangle group [ 2, 8, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^18 * G.2 * G.1 * G.3^19 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 75 action of group of order 416 via triangle group [ 2, 8, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^37 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^6 ] Genus 75 action of group of order 400 via triangle group [ 2, 8, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-18 * G.1 * G.3^18 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 75 action of group of order 400 via triangle group [ 2, 8, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-14 * G.1 * G.3^20 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 75 action of group of order 444 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 75 action of group of order 384 via triangle group [ 2, 12, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 75 action of group of order 384 via triangle group [ 2, 12, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-1 * G.1 * G.3^16 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-5 ] Genus 75 action of group of order 350 via triangle group [ 2, 14, 175 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.2^7 * G.3^-3, G.3^14 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-5 * G.1 * G.3^2 ] Genus 75 action of group of order 336 via triangle group [ 2, 21, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^2 * G.2^-1 * G.3^5 * G.2^-10 * G.3^3 ] Genus 75 action of group of order 330 via triangle group [ 2, 22, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^5 ] Genus 75 action of group of order 336 via triangle group [ 2, 24, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-10 * G.3^-1 * G.2 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-6 ] Genus 75 action of group of order 336 via triangle group [ 2, 24, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-10 * G.3^-1 * G.2 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 75 action of group of order 336 via triangle group [ 2, 28, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^9 * G.3^-2 * G.2 * G.3^-2 ] Genus 75 action of group of order 320 via triangle group [ 2, 32, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-2 * G.3^4 * G.2^-4 * G.3^4 ] Genus 75 action of group of order 320 via triangle group [ 2, 32, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-18 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 75 action of group of order 320 via triangle group [ 2, 40, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2^-3 * G.3 * G.2^-12 * G.3 * G.2^-1 * G.3 ] Genus 75 action of group of order 320 via triangle group [ 2, 40, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-7 * G.3^4 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 75 action of group of order 312 via triangle group [ 2, 52, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-19 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^17 * G.3^-1 ] Genus 75 action of group of order 310 via triangle group [ 2, 62, 155 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^4 * G.2 * G.3^-4 * G.1 * G.3, G.2^-17 * G.3^4 * G.2^-6 * G.3^2 * G.2^-1 * G.3 ] Genus 75 action of group of order 312 via triangle group [ 2, 78, 78 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-74 * G.3 * G.2^-1 ] Genus 75 action of group of order 302 via triangle group [ 2, 151, 302 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^108 * G.2^-42 ] Genus 75 action of group of order 304 via triangle group [ 2, 152, 152 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^43 * G.3^-108 * G.2 ] Genus 75 action of group of order 304 via triangle group [ 2, 152, 152 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-42 * G.2^2 * G.3^-1 * G.2^29 * G.3^-1 ] Genus 75 action of group of order 300 via triangle group [ 2, 300, 300 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^42 * G.3^-107 * G.2 ] Genus 75 action of group of order 888 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 75 action of group of order 888 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 ] Genus 75 action of group of order 453 via triangle group [ 3, 3, 151 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.3^4 * G.2^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 75 action of group of order 453 via triangle group [ 3, 3, 151 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.3^5 * G.1^-1 * G.2 * G.3^-7 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.1^-1 * G.3)^3, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.1^-1 * G.3)^3, G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 75 action of group of order 444 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^3 * G.3^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3^2 * G.2 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.3^-1 * G.1^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^2 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1 * G.3 * G.2^2 * G.3^-2, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 75 action of group of order 333 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.2^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 75 action of group of order 592 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 ] Genus 75 action of group of order 444 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 75 action of group of order 444 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 ] Genus 75 action of group of order 312 via triangle group [ 4, 4, 39 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-30 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^-7 ] Genus 75 action of group of order 304 via triangle group [ 4, 4, 76 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-30 * G.1^-1 * G.2^-1 * G.3^-7 ] Genus 75 action of group of order 304 via triangle group [ 4, 4, 76 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-30 * G.1^-1 * G.3 * G.2 * G.3^-6 ] Genus 75 action of group of order 304 via triangle group [ 4, 4, 76 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^60 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 75 action of group of order 304 via triangle group [ 4, 4, 76 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-24 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-7 ] Genus 75 action of group of order 300 via triangle group [ 4, 4, 150 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^59 * G.2^-1 * G.1 * G.3^15 ] Genus 75 action of group of order 336 via triangle group [ 4, 6, 7 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 ] Genus 75 action of group of order 336 via triangle group [ 4, 6, 7 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^3 * G.2^-1 * G.1^-1 * G.3^3 ] Genus 75 action of group of order 336 via triangle group [ 4, 6, 7 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-2)^2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 592 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 75 action of group of order 444 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-19 * G.2 * G.1 * G.3 * G.4^-19 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-39 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^31 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^32 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^31 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^5 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-26 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-25 * G.1 * G.2 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^30 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 75 action of group of order 312 via quadrangle group [ 2, 2, 2, 39 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^25 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-76 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-76 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-76 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-12 * G.2 * G.4 * G.3 * G.4^-13 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-6 * G.2 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^31 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^12 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-19 * G.1 * G.4^-5 * G.1 * G.4^-14 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-14 * G.2 * G.4^11 * G.1 * G.3 * G.4^-12 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^21 * G.3 * G.1 * G.3 * G.1 * G.4^15 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^14 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.4^12 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^16 * G.3 * G.4^-6 * G.1 * G.2 * G.4^15 ] Genus 75 action of group of order 304 via quadrangle group [ 2, 2, 2, 76 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-16 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^7 * G.2 * G.4^-8 ] Genus 75 action of group of order 300 via quadrangle group [ 2, 2, 2, 150 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-37 * G.2 * G.3 * G.4^-37 ] Genus 75 action of group of order 300 via quadrangle group [ 2, 2, 2, 150 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-68 * G.2 * G.4^-7 ] Genus 75 action of group of order 300 via quadrangle group [ 2, 2, 2, 150 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-60 * G.1 * G.2 * G.4^-14 ] Largest orientation-preserving group for genus 75 has order 1776 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 75 has order 1776 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 75 has order 1248 ... group action with signature (0; +; [-]; {(2,4,78)}) Largest chiral group for genus 75 has order 1776 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 76 has order 624 ... group action with signature (0; +; [-]; {(2,4,78)}) Check total 383 : 302 chiral, 81 reflexible, with 26 non-orientable quotient actions Genus 76 actions: Genus 76 action of group of order 1800 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 76 action of group of order 1500 via triangle group [ 2, 3, 15 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 76 action of group of order 1440 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.3^3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 76 action of group of order 1000 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^10, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 76 action of group of order 1000 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^10 ] Genus 76 action of group of order 616 via triangle group [ 2, 4, 154 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-32 * G.1 * G.2 * G.3^-121 ] Genus 76 action of group of order 608 via triangle group [ 2, 4, 304 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-31 * G.1 * G.2^-1 * G.3^-120 ] Genus 76 action of group of order 600 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 76 action of group of order 900 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 76 action of group of order 900 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 76 action of group of order 900 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 900 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 76 action of group of order 600 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 76 action of group of order 600 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 504 via triangle group [ 2, 6, 28 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-11 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-6 ] Genus 76 action of group of order 468 via triangle group [ 2, 6, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-11 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 76 action of group of order 468 via triangle group [ 2, 6, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-41 * G.1 * G.3 * G.2 * G.1 * G.3^21 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 76 action of group of order 468 via triangle group [ 2, 6, 78 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-44 * G.1 * G.3^12 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-19 ] Genus 76 action of group of order 456 via triangle group [ 2, 6, 228 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^62 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 76 action of group of order 450 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 76 action of group of order 432 via triangle group [ 2, 9, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^4 ] Genus 76 action of group of order 432 via triangle group [ 2, 9, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 76 action of group of order 432 via triangle group [ 2, 9, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3^3 * G.2^2 * G.3^-4 ] Genus 76 action of group of order 500 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-2, G.3^10 ] Genus 76 action of group of order 500 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^10, G.3^10 ] Genus 76 action of group of order 500 via triangle group [ 2, 10, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 76 action of group of order 500 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2^10, G.3^10 ] Genus 76 action of group of order 400 via triangle group [ 2, 10, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-16 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-7 ] Genus 76 action of group of order 400 via triangle group [ 2, 10, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-3 * G.1 * G.3^22 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 76 action of group of order 400 via triangle group [ 2, 10, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^10 ] Genus 76 action of group of order 380 via triangle group [ 2, 10, 190 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^26 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 76 action of group of order 360 via triangle group [ 2, 15, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-1 * G.3^3 * G.2^-5 * G.3^3 * G.2^-1 ] Genus 76 action of group of order 342 via triangle group [ 2, 18, 171 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-5 * G.3^4)^2, G.3^8 * G.2 * G.3^-4 * G.1 * G.3^6 ] Genus 76 action of group of order 360 via triangle group [ 2, 20, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-2 * G.2^4 * G.3^-4 ] Genus 76 action of group of order 336 via triangle group [ 2, 24, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-4 * G.2 * G.3 * G.2^-1 * G.3^-5 ] Genus 76 action of group of order 324 via triangle group [ 2, 54, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-20 * G.2 * G.3^-2 * G.2^9 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-13 * G.2^3 ] Genus 76 action of group of order 324 via triangle group [ 2, 54, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-21 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^15 * G.3^-3 ] Genus 76 action of group of order 312 via triangle group [ 2, 78, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-44 * G.2^2 * G.3^-1 * G.2^29 * G.3^-1 ] Genus 76 action of group of order 306 via triangle group [ 2, 153, 306 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^109 * G.2^-42 * G.3 ] Genus 76 action of group of order 308 via triangle group [ 2, 154, 154 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^44 * G.3^-110 ] Genus 76 action of group of order 304 via triangle group [ 2, 304, 304 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^43 * G.3^-109 ] Genus 76 action of group of order 900 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 76 action of group of order 720 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 76 action of group of order 468 via triangle group [ 3, 3, 78 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 76 action of group of order 468 via triangle group [ 3, 3, 78 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^5 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-1 * G.2 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 76 action of group of order 600 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 76 action of group of order 375 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 76 action of group of order 375 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 76 action of group of order 375 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-5, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 76 action of group of order 375 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 76 action of group of order 375 via triangle group [ 3, 5, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-5 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^-1 * G.3^2 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 76 action of group of order 450 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 ] Genus 76 action of group of order 360 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 312 via triangle group [ 3, 6, 52 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 76 action of group of order 312 via triangle group [ 3, 6, 52 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 76 action of group of order 500 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 308 via triangle group [ 4, 4, 77 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-68 * G.1^-1 * G.2^-1 * G.3^-8 ] Genus 76 action of group of order 304 via triangle group [ 4, 4, 152 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^60 * G.2^-1 * G.1 * G.3^15 ] Genus 76 action of group of order 360 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.2^-1 * G.1)^3, G.2^6 ] Genus 76 action of group of order 360 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.2^-1 * G.1)^3, G.2^6 ] Genus 76 action of group of order 360 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, (G.3^-1 * G.1)^3, G.3^6 ] Genus 76 action of group of order 360 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, (G.3^-1 * G.1)^3, G.3^6 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^10 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^10 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 76 action of group of order 900 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 76 action of group of order 600 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 500 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-13 * G.2 * G.1 * G.3 * G.4^-13 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^13 * G.3 * G.2 * G.4^2 * G.3 * G.4^-8 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^12 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.4^-2 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-9 * G.1 * G.4^2 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.4^-4 * G.2 * G.4^-7 * G.2 * G.4^-2 * G.2 * G.1 * G.4^5 * G.2 * G.4^6 * G.2 * G.4 ] Genus 76 action of group of order 324 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^6 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1 * G.3 * G.1 * G.4^-4 * G.2 * G.3 * G.2 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-38 * G.2 * G.1 * G.3 * G.4^-38 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-70 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 76 action of group of order 308 via quadrangle group [ 2, 2, 2, 77 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-62 * G.1 * G.2 * G.1 * G.2 * G.4^-13 ] Genus 76 action of group of order 304 via quadrangle group [ 2, 2, 2, 152 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-38 * G.1 * G.4^-38 ] Genus 76 action of group of order 304 via quadrangle group [ 2, 2, 2, 152 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-69 * G.1 * G.3 * G.4^-6 ] Genus 76 action of group of order 304 via quadrangle group [ 2, 2, 2, 152 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-61 * G.1 * G.2 * G.4^-14 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3^-1 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3 * G.4^-1 * G.3^-1 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3^-1)^4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.3^-1 * G.1 * G.4)^3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.4 * G.3)^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.4^-1 * G.2)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2, (G.3^-1 * G.1 * G.4)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3^-1 * G.1)^3, G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, (G.3 * G.1 * G.4)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.2)^4, (G.3 * G.2 * G.4)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3^-1 * G.4^-2 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.4^-1 * G.3)^3, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^2, (G.2 * G.1)^5 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3^-1)^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2^2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.1, G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 76 action of group of order 450 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.2^-1)^5 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.3 * G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, (G.3 * G.2^-1)^5 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, (G.2 * G.4 * G.3)^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2^-1 * G.1)^4, (G.2^-1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, (G.2^-1 * G.1)^4, G.4 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.4^-1 * G.2)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.2^-1)^3, (G.3 * G.1)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.1)^4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2 * G.4^-2 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.1 * G.2^-1)^5 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.4^-1 * G.2)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^2 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, (G.1 * G.2^-1)^5 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.2^-1 * G.4^2 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, G.2 * G.4 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2^-1 * G.3 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.4 * G.2^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.4^2 * G.2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.4^2 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 76 action of group of order 360 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 76 has order 1800 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 76 has order 3600 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 76 has order 3600 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 76 has order 900 ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 77 has order 1000 ... group action with signature (0; +; [-]; {(2,4,10)}) Check total 626 : 410 chiral, 216 reflexible, with 31 non-orientable quotient actions Genus 77 actions: Genus 77 action of group of order 672 via triangle group [ 2, 4, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-23 * G.1 * G.3^5 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-7 ] Genus 77 action of group of order 640 via triangle group [ 2, 4, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-64 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 77 action of group of order 640 via triangle group [ 2, 4, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-21 * G.1 * G.3^10 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 77 action of group of order 624 via triangle group [ 2, 4, 156 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-33 * G.1 * G.2 * G.3^-122 ] Genus 77 action of group of order 616 via triangle group [ 2, 4, 308 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-32 * G.1 * G.2^-1 * G.3^-121 ] Genus 77 action of group of order 912 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 77 action of group of order 912 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 77 action of group of order 912 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 ] Genus 77 action of group of order 912 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 77 action of group of order 570 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 77 action of group of order 570 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 77 action of group of order 480 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 77 action of group of order 480 via triangle group [ 2, 6, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 77 action of group of order 462 via triangle group [ 2, 6, 231 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-42 * G.1 * G.3^21 * G.2^-1 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 77 action of group of order 576 via triangle group [ 2, 8, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 77 action of group of order 448 via triangle group [ 2, 8, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^5 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-10 * G.1 * G.3^2 ] Genus 77 action of group of order 448 via triangle group [ 2, 8, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-4 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 77 action of group of order 416 via triangle group [ 2, 8, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^41 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 77 action of group of order 416 via triangle group [ 2, 8, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^37 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^3 ] Genus 77 action of group of order 480 via triangle group [ 2, 10, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^10, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 77 action of group of order 480 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.3^-1 * G.2 * G.3^-2 * G.2^3 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 77 action of group of order 480 via triangle group [ 2, 10, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4, G.2^10, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 77 action of group of order 480 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^10, G.1 * G.3 * G.2^-4 * G.3^-1 * G.2^3 * G.3^-1 ] Genus 77 action of group of order 456 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 77 action of group of order 456 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 77 action of group of order 456 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 77 action of group of order 384 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 77 action of group of order 384 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 77 action of group of order 384 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 77 action of group of order 384 via triangle group [ 2, 12, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2^12 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-4 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-4 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^6 * G.2 * G.3^-5 * G.1, G.2^2 * G.1 * G.3 * G.2 * G.1 * G.2^-6 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^3 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-5 * G.1 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^11 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 77 action of group of order 384 via triangle group [ 2, 16, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-10 ] Genus 77 action of group of order 352 via triangle group [ 2, 16, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 77 action of group of order 352 via triangle group [ 2, 16, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.1 * G.3^10 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 77 action of group of order 360 via triangle group [ 2, 18, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-2 * G.3 * G.2^-2 * G.3^4 ] Genus 77 action of group of order 360 via triangle group [ 2, 20, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-6, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 77 action of group of order 336 via triangle group [ 2, 24, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-10 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 77 action of group of order 336 via triangle group [ 2, 24, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2 * G.1 * G.3^5 ] Genus 77 action of group of order 336 via triangle group [ 2, 28, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-14 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 77 action of group of order 330 via triangle group [ 2, 30, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^7 * G.2^-4 * G.3^4 ] Genus 77 action of group of order 336 via triangle group [ 2, 42, 42 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^-3 * G.3^22 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-10 * G.3^2 ] Genus 77 action of group of order 336 via triangle group [ 2, 42, 42 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^24 * G.2^-15 ] Genus 77 action of group of order 336 via triangle group [ 2, 42, 42 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-42 ] Genus 77 action of group of order 322 via triangle group [ 2, 46, 161 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1, G.2^-10 * G.3^4 * G.2^-6 * G.3^3 ] Genus 77 action of group of order 320 via triangle group [ 2, 80, 80 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-47 * G.2^30 * G.3^-1 * G.2 ] Genus 77 action of group of order 320 via triangle group [ 2, 80, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-7 * G.2 * G.3^-1 * G.2^11 * G.3^-3 * G.2 * G.3^-13 * G.2^3 ] Genus 77 action of group of order 320 via triangle group [ 2, 80, 80 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-23 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 77 action of group of order 320 via triangle group [ 2, 80, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-6 * G.2 * G.3^-1 * G.2^10 * G.3^-4 * G.2^15 * G.3^-3 ] Genus 77 action of group of order 310 via triangle group [ 2, 155, 310 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^110 * G.2^-44 ] Genus 77 action of group of order 312 via triangle group [ 2, 156, 156 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^45 * G.3^-110 * G.2 ] Genus 77 action of group of order 308 via triangle group [ 2, 308, 308 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^44 * G.3^-109 * G.2 ] Genus 77 action of group of order 456 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 77 action of group of order 456 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 77 action of group of order 456 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-2 * G.2^2 * G.3^-2 ] Genus 77 action of group of order 456 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-2 * G.2^2 * G.3^-2 ] Genus 77 action of group of order 336 via triangle group [ 3, 7, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^-7, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 ] Genus 77 action of group of order 336 via triangle group [ 4, 4, 21 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-7 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 ] Genus 77 action of group of order 336 via triangle group [ 4, 4, 21 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^21 ] Genus 77 action of group of order 336 via triangle group [ 4, 4, 21 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^7 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-9 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-28 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-5 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-10 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^9 * G.2 * G.3^-1 * G.1 * G.3^9 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-6 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-6 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-9 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^5 * G.2 * G.3^-5 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^3 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^26 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^8 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^13 * G.2 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^8 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^9 * G.2 * G.3^-2 * G.1^-1 * G.3^8 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^28 * G.2 * G.3^-6 * G.1^-1 * G.3^5 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^6 * G.2^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-7 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^8 * G.2 * G.3^-1 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^9 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.1 * G.3 * G.2^-2 * G.1 * G.3^-3 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 77 action of group of order 320 via triangle group [ 4, 4, 40 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 77 action of group of order 312 via triangle group [ 4, 4, 78 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-61 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 77 action of group of order 312 via triangle group [ 4, 4, 78 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^-3 ] Genus 77 action of group of order 312 via triangle group [ 4, 4, 78 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-2, G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 77 action of group of order 308 via triangle group [ 4, 4, 154 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-68 * G.1^-1 * G.2 * G.3^-8 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^38 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^38 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 608 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 380 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3, (G.1 * G.3)^6 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, (G.1 * G.2)^6 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-10 * G.2 * G.1 * G.3 * G.4^-10 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^7 * G.3 * G.4^-5 * G.1 * G.2 * G.4^8 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^7 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^4 * G.2 * G.4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-8 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-8 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^13 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-11 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 77 action of group of order 336 via quadrangle group [ 2, 2, 2, 21 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-40 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-17 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-12 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^23 * G.3 * G.1 * G.3 * G.1^2 * G.4^-9 * G.1 * G.4^6 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^14 * G.2 * G.4^-12 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^28 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^23 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4^8 * G.3 * G.4^-1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-8 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-5 * G.1 * G.4^2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^9 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-8 * G.1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-7 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-10 * G.1 * G.4^-2 * G.1 * G.4^-8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^9 * G.3 * G.4^-1 * G.1 * G.4^-5 * G.2 * G.4^4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-6 * G.2 * G.4^7 * G.3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4^11 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-12 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^7 * G.3 * G.2 * G.1 * G.4^4 * G.2 * G.4^-4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^9 * G.2 * G.4^-4 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.4^2 * G.2 * G.4^4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-7 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^7 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-7 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-10 * G.1 * G.4^-2 * G.1 * G.4^-8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-3 * G.2 * G.4^5 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1^2 * G.4^-3 * G.1 * G.3 * G.4^-6 * G.1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4^-4 * G.1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^11 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^11 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.2 * G.4^-2 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.4^11 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-9 * G.2 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.4^-2 * G.1 * G.4^8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^6 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^11 * G.3 * G.4^-1 * G.1 * G.2 * G.4^7 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-7 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^3 * G.3 * G.4^-4 * G.2 * G.4^2 * G.3 * G.4^-7 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-11 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-6 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^10 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^9 * G.1 * G.4 * G.1^2 * G.3 * G.4^-9 * G.2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.4^-8 * G.1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-3 * G.1 * G.4^5 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-5 * G.1 * G.2 * G.1 * G.4^6 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^12 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.4^-6 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-8 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^13 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-13 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^13 * G.3 * G.4^-1 * G.2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-35 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.1 * G.2 * G.4^-11 * G.1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-8 * G.1 * G.3 * G.4^-8 * G.1 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-8 * G.2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-13 * G.2 * G.4 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-13 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-13 * G.1 * G.3 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.4^-3 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-15 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^4 * G.1 * G.3 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^4 * G.1 * G.3 * G.2 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 320 via quadrangle group [ 2, 2, 2, 40 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-12 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^16 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-13 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^16 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-34 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^33 * G.3 * G.1 * G.4^5 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-14 * G.1 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-14 * G.1 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-13 * G.1 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-8 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^11 * G.1 * G.3 * G.4^-12 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^13 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.4^12 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.4^-10 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.4^6 * G.2 * G.4^2 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-3 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^7 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-78 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-78 ] Genus 77 action of group of order 312 via quadrangle group [ 2, 2, 2, 78 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^47 * G.2 * G.4^-15 * G.1 * G.2 * G.1 * G.4^14 ] Genus 77 action of group of order 308 via quadrangle group [ 2, 2, 2, 154 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-38 * G.2 * G.3 * G.4^-38 ] Genus 77 action of group of order 308 via quadrangle group [ 2, 2, 2, 154 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-70 * G.2 * G.4^-7 ] Genus 77 action of group of order 308 via quadrangle group [ 2, 2, 2, 154 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-62 * G.1 * G.2 * G.4^-14 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.3 * G.1 * G.3 * G.4^-1)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.3^-1 * G.4 * G.2 * G.4)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.3^-1 * G.4 * G.2 * G.4)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.3 * G.1 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.3 * G.2 * G.4^-2 * G.3 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1^2 * G.2 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1^2 * G.2 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 77 action of group of order 456 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Largest orientation-preserving group for genus 77 has order 912 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 77 has order 1344 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest group with reflections for genus 77 has order 1344 ... group action with signature (0; +; [-]; {(2,4,42)}) Largest chiral group for genus 77 has order 912 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 78 has order 608 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 1127 : 846 chiral, 281 reflexible, with 79 non-orientable quotient actions Genus 78 actions: Genus 78 action of group of order 1176 via triangle group [ 2, 3, 28 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^15 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 78 action of group of order 648 via triangle group [ 2, 4, 81 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-64 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 78 action of group of order 632 via triangle group [ 2, 4, 158 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-34 * G.1 * G.2 * G.3^-123 ] Genus 78 action of group of order 624 via triangle group [ 2, 4, 312 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-33 * G.1 * G.2^-1 * G.3^-122 ] Genus 78 action of group of order 588 via triangle group [ 2, 6, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^14 ] Genus 78 action of group of order 588 via triangle group [ 2, 6, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^14 ] Genus 78 action of group of order 480 via triangle group [ 2, 6, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-66 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 78 action of group of order 432 via triangle group [ 2, 8, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^34 * G.2 * G.3^-9 * G.1 * G.3^10 ] Genus 78 action of group of order 432 via triangle group [ 2, 8, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-8 * G.1 * G.3 * G.2^-1 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^10, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-4 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2^10, G.3^-3 * G.2^3 * G.3^-1 * G.2 * G.3^-2 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^10, G.2^2 * G.3^-1 * G.2^3 * G.3^-2 * G.2 * G.3^-1 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^10, G.2 * G.3^-2 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^10, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2^10, G.3^-2 * G.2^4 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 78 action of group of order 440 via triangle group [ 2, 10, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-3 * G.2 ] Genus 78 action of group of order 390 via triangle group [ 2, 10, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^24 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 ] Genus 78 action of group of order 384 via triangle group [ 2, 12, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-1 * G.1 * G.3^16 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 78 action of group of order 392 via triangle group [ 2, 14, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-8 * G.3 * G.1 * G.2^-5 ] Genus 78 action of group of order 392 via triangle group [ 2, 14, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-2 * G.3^4 * G.2^-1)^2, G.3^9 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-13 * G.1 ] Genus 78 action of group of order 392 via triangle group [ 2, 14, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^-6 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-6 ] Genus 78 action of group of order 364 via triangle group [ 2, 14, 182 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-2 * G.3^4 * G.2^-1)^2, G.1 * G.3^7 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-13 ] Genus 78 action of group of order 360 via triangle group [ 2, 20, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 78 action of group of order 336 via triangle group [ 2, 28, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2^-2 * G.3^4 ] Genus 78 action of group of order 336 via triangle group [ 2, 42, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2^-3 * G.3^3 ] Genus 78 action of group of order 336 via triangle group [ 2, 42, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.2^9 * G.3^-1 * G.2^3 * G.3^-1 ] Genus 78 action of group of order 324 via triangle group [ 2, 81, 81 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-77 * G.3 * G.2^-1 ] Genus 78 action of group of order 318 via triangle group [ 2, 106, 159 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-20 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^16 * G.3^-1 * G.2 ] Genus 78 action of group of order 314 via triangle group [ 2, 157, 314 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^111 * G.2^-44 * G.3 ] Genus 78 action of group of order 316 via triangle group [ 2, 158, 158 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^46 * G.3^-112 ] Genus 78 action of group of order 312 via triangle group [ 2, 312, 312 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^45 * G.3^-111 ] Genus 78 action of group of order 588 via triangle group [ 3, 3, 14 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-14 ] Genus 78 action of group of order 471 via triangle group [ 3, 3, 157 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2^-1 * G.3^-1 * G.1^2 * G.3^5 ] Genus 78 action of group of order 471 via triangle group [ 3, 3, 157 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-6 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 78 action of group of order 316 via triangle group [ 4, 4, 79 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-62 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 78 action of group of order 312 via triangle group [ 4, 4, 156 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-61 * G.1 * G.2^-1 * G.3^-16 ] Genus 78 action of group of order 336 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-2)^2, G.2^6, G.3^2 * G.2 * G.1 * G.3^-1 * G.1^-1 ] Genus 78 action of group of order 336 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.3^2 * G.2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3 ] Genus 78 action of group of order 336 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 78 action of group of order 336 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, (G.3^-1 * G.2)^3 ] Genus 78 action of group of order 316 via quadrangle group [ 2, 2, 2, 79 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-39 * G.2 * G.1 * G.3 * G.4^-39 ] Genus 78 action of group of order 316 via quadrangle group [ 2, 2, 2, 79 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-72 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 78 action of group of order 316 via quadrangle group [ 2, 2, 2, 79 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^66 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 78 action of group of order 312 via quadrangle group [ 2, 2, 2, 156 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-39 * G.1 * G.4^-39 ] Genus 78 action of group of order 312 via quadrangle group [ 2, 2, 2, 156 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-71 * G.1 * G.3 * G.4^-6 ] Genus 78 action of group of order 312 via quadrangle group [ 2, 2, 2, 156 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^63 * G.2 * G.1 * G.4^14 ] Largest orientation-preserving group for genus 78 has order 1176 ... group action with signature (0: +; [2,3,28]; {-}) Largest group with or without reflections for genus 78 has order 2352 ... group action with signature (0; +; [-]; {(2,3,28)}) Largest group with reflections for genus 78 has order 2352 ... group action with signature (0; +; [-]; {(2,3,28)}) Largest chiral group for genus 78 has order 440 ... group action with signature (0: +; [2,10,20]; {-}) Largest non-orientable group for non-orientable genus 79 has order 648 ... group action with signature (0; +; [-]; {(2,4,81)}) Check total 47 : 8 chiral, 39 reflexible, with 11 non-orientable quotient actions Genus 79 actions: Genus 79 action of group of order 1872 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 1872 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 79 action of group of order 832 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2, G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 79 action of group of order 832 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^6 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 * G.1 * G.3 ] Genus 79 action of group of order 832 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 832 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 728 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2, G.3 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 79 action of group of order 728 via triangle group [ 2, 4, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 79 action of group of order 720 via triangle group [ 2, 4, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-4)^2 ] Genus 79 action of group of order 640 via triangle group [ 2, 4, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-35 * G.1 * G.2 * G.3^-124 ] Genus 79 action of group of order 640 via triangle group [ 2, 4, 160 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-72 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 79 action of group of order 632 via triangle group [ 2, 4, 316 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-34 * G.1 * G.2^-1 * G.3^-123 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 79 action of group of order 702 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 79 action of group of order 624 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 79 action of group of order 624 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 79 action of group of order 546 via triangle group [ 2, 6, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 79 action of group of order 546 via triangle group [ 2, 6, 21 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 486 via triangle group [ 2, 6, 81 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^44 * G.2 * G.1 * G.3^22 * G.2^-1 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^4 ] Genus 79 action of group of order 486 via triangle group [ 2, 6, 81 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^8 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 79 action of group of order 486 via triangle group [ 2, 6, 81 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^7 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 79 action of group of order 474 via triangle group [ 2, 6, 237 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-44 * G.1 * G.3^21 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 79 action of group of order 672 via triangle group [ 2, 7, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 480 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 79 action of group of order 480 via triangle group [ 2, 8, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 79 action of group of order 432 via triangle group [ 2, 9, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.3 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^12, G.3 * G.2 * G.3^-1 * G.2^4 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 79 action of group of order 432 via triangle group [ 2, 12, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^12, G.1 * G.3 * G.2^5 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 79 action of group of order 384 via triangle group [ 2, 12, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 79 action of group of order 384 via triangle group [ 2, 12, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-1 * G.1 * G.3^14 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 79 action of group of order 390 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3^2 * G.2^-4 * G.3^3 * G.2^-1 * G.3 * G.2^-1 ] Genus 79 action of group of order 390 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 79 action of group of order 416 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, (G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1)^2 ] Genus 79 action of group of order 416 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 79 action of group of order 416 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-2 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 ] Genus 79 action of group of order 416 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 79 action of group of order 364 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 79 action of group of order 364 via triangle group [ 2, 28, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-2 ] Genus 79 action of group of order 360 via triangle group [ 2, 30, 30 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-4 * G.3^-4 ] Genus 79 action of group of order 336 via triangle group [ 2, 42, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-2 * G.3^3 * G.2^-13 * G.3^3 ] Genus 79 action of group of order 318 via triangle group [ 2, 159, 318 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^112 * G.2^-46 ] Genus 79 action of group of order 320 via triangle group [ 2, 160, 160 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^47 * G.3^-112 * G.2 ] Genus 79 action of group of order 320 via triangle group [ 2, 160, 160 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-47 * G.2^31 * G.3^-1 ] Genus 79 action of group of order 316 via triangle group [ 2, 316, 316 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^46 * G.3^-111 * G.2 ] Genus 79 action of group of order 936 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 79 action of group of order 936 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 504 via triangle group [ 3, 3, 42 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 79 action of group of order 504 via triangle group [ 3, 3, 42 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1 ] Genus 79 action of group of order 624 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-2 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 79 action of group of order 468 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 79 action of group of order 360 via triangle group [ 3, 5, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^2 * G.2^-2 * G.1 * G.2^-1 * G.3^2 ] Genus 79 action of group of order 360 via triangle group [ 3, 6, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 79 action of group of order 360 via triangle group [ 3, 6, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 360 via triangle group [ 3, 6, 15 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 79 action of group of order 336 via triangle group [ 3, 6, 28 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 79 action of group of order 336 via triangle group [ 3, 6, 28 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 79 action of group of order 351 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 * G.1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 79 action of group of order 416 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 ] Genus 79 action of group of order 364 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 79 action of group of order 364 via triangle group [ 4, 4, 14 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 79 action of group of order 360 via triangle group [ 4, 4, 15 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, (G.1 * G.3^-2)^2, (G.2 * G.3^-2)^2 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-63 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-27 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-28 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^26 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.1 * G.3^8 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-27 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-5 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^28 * G.2^-1 * G.3^-6 * G.1^-1 * G.3^5 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-9 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-9 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 79 action of group of order 320 via triangle group [ 4, 4, 80 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 79 action of group of order 316 via triangle group [ 4, 4, 158 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-62 * G.1 * G.2^-1 * G.3^-16 ] Genus 79 action of group of order 336 via triangle group [ 4, 7, 7 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-7, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, (G.3 * G.1)^26 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^39 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 624 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^39 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^26 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 468 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 416 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^14, G.1 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-6 * G.2 * G.1 * G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^5 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 364 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.4^3, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^-3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.4^3 * G.2 * G.1 * G.4^5, G.4 * G.3 * G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, (G.1 * G.4^4 * G.2)^2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.1, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^5 * G.1 * G.3 * G.4^-4 * G.2, G.2 * G.3 * G.2 * G.4^2 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2 * G.4^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.3 * G.1 * G.4)^3, G.1 * G.4^3 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.4^-5 * G.2 * G.1 * G.4^4 * G.3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.4, G.4^-5 * G.2 * G.1 * G.4^4 * G.3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.4^2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1 * G.4)^3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 79 action of group of order 360 via quadrangle group [ 2, 2, 2, 15 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1^2 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.4^6 * G.3 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.3 * G.4^-9 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^5 * G.3 * G.4^-4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^8 * G.1 * G.4^-1 * G.1 * G.4^5 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.4^5 * G.1 * G.3 * G.1 * G.4^6 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^7 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^22 * G.1^2 * G.4^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-17 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^14 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-12 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-28 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-28 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^23 * G.1^2 * G.4^5 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^3 * G.3 * G.4^-10 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^5 * G.2 * G.4^4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-3 * G.1 * G.4^9 * G.3 * G.4^-4 * G.2 * G.4^-11 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^9 * G.2 * G.1 * G.2 * G.1 * G.4^17 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-14 * G.1 * G.4^7 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-10 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-8 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-10 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^4 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.1 * G.4^-1 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.3 * G.1^2 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^6 * G.3 * G.1 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^7 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-3 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^7 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^6 * G.3 * G.1 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.4^6 * G.3 * G.4^-6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-6 * G.1 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^8 * G.1 * G.4^-1 * G.1 * G.4^5 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^7 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4^4 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-6 * G.1 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-7 * G.1 * G.4 * G.2 * G.4^4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.4 * G.3 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4^4 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-3 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.4^5 * G.1 * G.3 * G.1 * G.4^6 * G.2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, (G.1 * G.3)^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 79 action of group of order 336 via quadrangle group [ 2, 2, 2, 28 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^15 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^17 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^13 * G.1^2 * G.3 * G.4^-13 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-13 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-12 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^10 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-11 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^-8 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^10 * G.3 * G.4^-2 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^20 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-21 * G.1 * G.3 * G.4^-5 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-11 * G.1 * G.4^11 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-14 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-10 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-12 * G.1 * G.2 * G.1 * G.4^6 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 79 action of group of order 324 via quadrangle group [ 2, 2, 2, 54 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^9 * G.2 * G.1 * G.4^17 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-80 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-80 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^67 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-13 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^16 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^33 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-10 * G.1 * G.4 * G.2 * G.4^-27 * G.1 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-20 * G.1 * G.4^-5 * G.1 * G.4^-15 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-21 * G.2 * G.4^6 * G.1 * G.3 * G.4^-12 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^23 * G.3 * G.1 * G.3 * G.1 * G.4^15 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^16 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.4^12 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^29 * G.3 * G.1 * G.2 * G.4^10 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^18 * G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^5 * G.1 * G.4^-5, G.4^-8 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-4 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^5)^2, G.4^-6 * G.1 * G.4^3 * G.1 * G.4^-7 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^6 * G.2 * G.1 * G.4^2 * G.1^2 * G.2 * G.1 * G.4^6 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^10 * G.1^2 * G.2 * G.4^3 * G.2 * G.4^3 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^6 * G.1 * G.3 * G.2 * G.4^3 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^6 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^4 * G.1 * G.3 * G.2 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^4 * G.1 * G.4 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3 ] Genus 79 action of group of order 320 via quadrangle group [ 2, 2, 2, 80 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 79 action of group of order 316 via quadrangle group [ 2, 2, 2, 158 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-39 * G.2 * G.3 * G.4^-39 ] Genus 79 action of group of order 316 via quadrangle group [ 2, 2, 2, 158 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-72 * G.2 * G.4^-7 ] Genus 79 action of group of order 316 via quadrangle group [ 2, 2, 2, 158 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^67 * G.1^2 * G.2 * G.1 * G.4^11 ] Largest orientation-preserving group for genus 79 has order 1872 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 79 has order 1872 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 79 has order 1440 ... group action with signature (0; +; [-]; {(2,4,30)}) Largest chiral group for genus 79 has order 1872 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 80 has order 624 ... group action with signature (0; +; [-]; {(2,2,2,4)}) ... group action with signature (0; +; [2]; {(2,4)}) Check total 1030 : 794 chiral, 236 reflexible, with 79 non-orientable quotient actions Genus 80 actions: Genus 80 action of group of order 648 via triangle group [ 2, 4, 162 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-36 * G.1 * G.2 * G.3^-125 ] Genus 80 action of group of order 640 via triangle group [ 2, 4, 320 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-35 * G.1 * G.2^-1 * G.3^-124 ] Genus 80 action of group of order 948 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 80 action of group of order 948 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 80 action of group of order 948 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 ] Genus 80 action of group of order 948 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 ] Genus 80 action of group of order 492 via triangle group [ 2, 6, 82 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-82 ] Genus 80 action of group of order 480 via triangle group [ 2, 6, 240 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-44 * G.1 * G.3^22 * G.2^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-5 ] Genus 80 action of group of order 432 via triangle group [ 2, 8, 108 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^34 * G.2 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.3^11 ] Genus 80 action of group of order 420 via triangle group [ 2, 10, 42 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^27 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^6 ] Genus 80 action of group of order 408 via triangle group [ 2, 12, 34 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^19 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^6 ] Genus 80 action of group of order 384 via triangle group [ 2, 12, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-2 * G.1 * G.3^9 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-16 ] Genus 80 action of group of order 396 via triangle group [ 2, 18, 22 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-3 ] Genus 80 action of group of order 360 via triangle group [ 2, 18, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 80 action of group of order 360 via triangle group [ 2, 20, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^9 * G.2 * G.3^-2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 80 action of group of order 352 via triangle group [ 2, 22, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-9 * G.3^4 * G.2^-5 * G.3^4 ] Genus 80 action of group of order 340 via triangle group [ 2, 34, 170 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.2^-20 * G.3^4 * G.2^-5 * G.3^4 * G.2^-1 ] Genus 80 action of group of order 336 via triangle group [ 2, 42, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-6 * G.2 * G.3^-1 * G.2^10 * G.3^-4 * G.2^18 * G.3^-1 ] Genus 80 action of group of order 336 via triangle group [ 2, 56, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-1 * G.2^6 * G.3^-5 * G.2 ] Genus 80 action of group of order 330 via triangle group [ 2, 66, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^3 * G.2^-16 * G.3^4 * G.2^-5 * G.3^3 * G.2^-1 * G.3 ] Genus 80 action of group of order 328 via triangle group [ 2, 82, 164 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-48 * G.2^33 ] Genus 80 action of group of order 322 via triangle group [ 2, 161, 322 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^113 * G.2^-46 * G.3 ] Genus 80 action of group of order 324 via triangle group [ 2, 162, 162 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^48 * G.3^-114 ] Genus 80 action of group of order 320 via triangle group [ 2, 320, 320 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^47 * G.3^-113 ] Genus 80 action of group of order 474 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 80 action of group of order 474 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 80 action of group of order 474 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 80 action of group of order 474 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 80 action of group of order 336 via triangle group [ 3, 8, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^8, G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 80 action of group of order 336 via triangle group [ 3, 8, 14 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.2^-1 * G.3, G.2^8, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 80 action of group of order 324 via triangle group [ 4, 4, 81 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-64 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 80 action of group of order 320 via triangle group [ 4, 4, 160 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-63 * G.1 * G.2^-1 * G.3^-16 ] Genus 80 action of group of order 324 via quadrangle group [ 2, 2, 2, 81 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-40 * G.2 * G.1 * G.3 * G.4^-40 ] Genus 80 action of group of order 324 via quadrangle group [ 2, 2, 2, 81 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-74 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 80 action of group of order 324 via quadrangle group [ 2, 2, 2, 81 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^69 * G.1^2 * G.4^12 ] Genus 80 action of group of order 320 via quadrangle group [ 2, 2, 2, 160 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-40 * G.1 * G.4^-40 ] Genus 80 action of group of order 320 via quadrangle group [ 2, 2, 2, 160 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-73 * G.1 * G.3 * G.4^-6 ] Genus 80 action of group of order 320 via quadrangle group [ 2, 2, 2, 160 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^67 * G.2 * G.1 * G.4^12 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2^2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^2 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1, G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^2 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 80 action of group of order 474 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 ] Largest orientation-preserving group for genus 80 has order 948 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 80 has order 1296 ... group action with signature (0; +; [-]; {(2,4,162)}) Largest group with reflections for genus 80 has order 1296 ... group action with signature (0; +; [-]; {(2,4,162)}) Largest chiral group for genus 80 has order 948 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 81 has order 492 ... group action with signature (0; +; [-]; {(2,6,82)}) Check total 358 : 320 chiral, 38 reflexible, with 9 non-orientable quotient actions Genus 81 actions: Genus 81 action of group of order 1536 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.3^8 * G.2 * G.3^-1 * G.1^2 * G.2^-1 * G.3^-1 * G.1 * G.3^7 ] Genus 81 action of group of order 1536 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 1536 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-4 * G.1 * G.3 ] Genus 81 action of group of order 1536 via triangle group [ 2, 3, 16 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3^5 ] Genus 81 action of group of order 1320 via triangle group [ 2, 3, 22 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 1280 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 1152 via triangle group [ 2, 4, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-2)^4, G.3^12, G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^4, G.3^12, G.2^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-1)^6, (G.2 * G.3^-3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 960 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 81 action of group of order 800 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-12 * G.1 * G.2 * G.3^-7 ] Genus 81 action of group of order 800 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 81 action of group of order 800 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.2, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.2, G.3^-6 * G.1 * G.3^6 * G.2 * G.3^-11 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4, (G.2 * G.3^-5)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-7 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.3^-8 * G.1 * G.3^4 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3^7 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^2 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3^12 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^-3 * G.1 * G.3^8 * G.2 * G.3^-12 ] Genus 81 action of group of order 768 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 720 via triangle group [ 2, 4, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-9 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 720 via triangle group [ 2, 4, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-11 * G.1 * G.3^12 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 704 via triangle group [ 2, 4, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-25 * G.1 * G.3^11 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 680 via triangle group [ 2, 4, 68 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-13 * G.1 * G.3^9 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 680 via triangle group [ 2, 4, 68 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-13 * G.1 * G.3 * G.2 * G.1 * G.3^6 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 672 via triangle group [ 2, 4, 84 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-67 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 81 action of group of order 672 via triangle group [ 2, 4, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-25 * G.1 * G.3^7 * G.2^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 81 action of group of order 672 via triangle group [ 2, 4, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-68 * G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 81 action of group of order 656 via triangle group [ 2, 4, 164 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-37 * G.1 * G.2 * G.3^-126 ] Genus 81 action of group of order 648 via triangle group [ 2, 4, 324 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-36 * G.1 * G.2^-1 * G.3^-125 ] Genus 81 action of group of order 1200 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 800 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 81 action of group of order 600 via triangle group [ 2, 5, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 81 action of group of order 600 via triangle group [ 2, 5, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2^2 * G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, (G.3 * G.2^-1 * G.3)^3, G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-3 * G.2^2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.1, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^-2 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-1 * G.2 * G.3^-3 * G.2^2 * G.3^-3 * G.2 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2, (G.2 * G.3^-1 * G.2)^4, G.3^-2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3, (G.2 * G.3^-1 * G.2)^4, G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, (G.2 * G.3^-1 * G.2)^4 ] Genus 81 action of group of order 768 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 ] Genus 81 action of group of order 660 via triangle group [ 2, 6, 11 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-5 * G.1 * G.2 * G.3^-5 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.3^-3 * G.2^3 * G.3^-2 * G.2^2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2 * G.3^-2 * G.2^3 * G.3^-3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.3^-3 * G.2^3 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^8, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 640 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^5 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-7 * G.1 * G.2^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.3^4 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-2 * G.1 * G.2^-3 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-2 * G.1 * G.2^-3 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^-16 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-2 * G.1 * G.2^-3 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.3^-7 * G.2^2 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-3 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^3 * G.2^-3 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-3 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.3^2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-4 * G.3^-2 * G.2^3, G.3^-2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.3^-2 * G.1 * G.3^4 * G.2 * G.3^-9 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-5 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 512 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 480 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^4 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-18 * G.1 * G.3^21 * G.2 * G.3^-2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-12 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^36 * G.2 * G.3^-9 * G.1 * G.3^10 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^7 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-11 * G.1 ] Genus 81 action of group of order 448 via triangle group [ 2, 8, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^5 * G.2 * G.1 * G.3^6 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 81 action of group of order 432 via triangle group [ 2, 8, 216 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^40 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 432 via triangle group [ 2, 8, 216 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^38 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 576 via triangle group [ 2, 9, 9 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-9, (G.2^-2 * G.3)^3, (G.3 * G.2^-1 * G.3)^3 ] Genus 81 action of group of order 480 via triangle group [ 2, 10, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-3 * G.2)^2, G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.2^-4 * G.3^-1 * G.2 * G.3^-3, G.2^12 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1 * G.2^-3 * G.3 * G.2^-1 * G.3^-3, G.2^12 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-3 * G.3^-2 * G.2^2, G.2^-1 * G.3^2 * G.2^-2 * G.3^-3 * G.1 ] Genus 81 action of group of order 378 via triangle group [ 2, 14, 189 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-2 * G.3^4 * G.2^-1)^2, G.3^14 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2^-2 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, (G.2 * G.3^-1)^4 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-4 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.2^-1 * G.3^-5 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^2 * G.3^-2 * G.2^7 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^4 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-10 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.2 * G.1 * G.3^11 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-5 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-5 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.2^2 * G.3^-2 * G.2^7 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 2, 16, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-5 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 400 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3^3 ] Genus 81 action of group of order 400 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 81 action of group of order 400 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-8 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 400 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3^2 * G.2^-1 * G.3^4 * G.2^-4 * G.3 * G.2^-6 * G.3, G.2^2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-4 * G.3 * G.2^5 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 400 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-2 * G.3 * G.2^10 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-4, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 360 via triangle group [ 2, 20, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-7 * G.3^4 * G.2^-5 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-6 * G.3^3 * G.2^-10 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^-1 * G.3^3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-7 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-1 * G.2 * G.3^-2 * G.2, G.2^7 * G.3^-2 * G.2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2^7 * G.3^-2 * G.2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-3 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-12 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-1 * G.2^6 * G.3^-5 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-5, G.2^7 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^7 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-3 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-9 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^2 * G.3^-1 * G.2^4 * G.3^-3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.2^6 * G.3^-5 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2^-4 * G.3^-1 * G.2 * G.1 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-9 * G.3^3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-6 * G.3 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.2 * G.3^-4 * G.2^3 * G.3^-1 * G.2^6 * G.3^-3 * G.2 * G.3^-2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2^6 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5, G.2 * G.3^-1 * G.2^5 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.3^-1 * G.2^6 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.2 * G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-1 * G.2^5 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 350 via triangle group [ 2, 35, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2 * G.3^-2 * G.2^13 * G.3^-1 * G.2 * G.3^-15 * G.2^2 ] Genus 81 action of group of order 360 via triangle group [ 2, 36, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^17 * G.3^-4 * G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-2 ] Genus 81 action of group of order 360 via triangle group [ 2, 36, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-17 * G.2^3 * G.3^-2 * G.2^6 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 ] Genus 81 action of group of order 342 via triangle group [ 2, 38, 171 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-6 * G.3^4 * G.2^-4 * G.3^5 ] Genus 81 action of group of order 352 via triangle group [ 2, 44, 44 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-27 * G.3^3 * G.2^-10 * G.3^2 ] Genus 81 action of group of order 336 via triangle group [ 2, 56, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-23 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^18 * G.3^-1 ] Genus 81 action of group of order 336 via triangle group [ 2, 56, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.3^4 * G.2^-10 * G.3^4 * G.2^-5 * G.3^3 * G.2^-1 * G.3 ] Genus 81 action of group of order 340 via triangle group [ 2, 68, 68 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^-13 * G.3^5 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-6 * G.3^2 * G.2^-2 * G.3 ] Genus 81 action of group of order 340 via triangle group [ 2, 68, 68 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3^12 * G.2^-6 * G.3 * G.2^-10 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 336 via triangle group [ 2, 84, 84 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-80 * G.3 * G.2^-1 ] Genus 81 action of group of order 336 via triangle group [ 2, 84, 84 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-39 * G.3^3 ] Genus 81 action of group of order 336 via triangle group [ 2, 84, 84 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-50 * G.2^31 * G.3^-2 ] Genus 81 action of group of order 330 via triangle group [ 2, 110, 165 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-21 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^19 ] Genus 81 action of group of order 326 via triangle group [ 2, 163, 326 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^114 * G.2^-48 ] Genus 81 action of group of order 328 via triangle group [ 2, 164, 164 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^49 * G.3^-114 * G.2 ] Genus 81 action of group of order 324 via triangle group [ 2, 324, 324 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^48 * G.3^-113 * G.2 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3^8 ] Genus 81 action of group of order 768 via triangle group [ 3, 3, 8 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^8, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 81 action of group of order 660 via triangle group [ 3, 3, 11 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^2 ] Genus 81 action of group of order 525 via triangle group [ 3, 3, 35 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^4 * G.2 * G.1^-2 * G.3 * G.2 * G.3^-6 ] Genus 81 action of group of order 525 via triangle group [ 3, 3, 35 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2 * G.1 * G.3^5 ] Genus 81 action of group of order 489 via triangle group [ 3, 3, 163 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3^3 * G.2 * G.3^-5 ] Genus 81 action of group of order 489 via triangle group [ 3, 3, 163 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 81 action of group of order 600 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2, G.3^2 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1)^2, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^8, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.2^8, (G.1 * G.3 * G.2^2)^2, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2^3 * G.1^-1 * G.3^3, G.2^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2^3 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^8, G.1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^8, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2^3 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1 * G.2^-2 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2, G.2^8, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.2 * G.1 * G.2^-2 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2, G.2^8, (G.1 * G.3 * G.2^2)^2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1 * G.2^-2 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^2 * G.2)^2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-3, G.3^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^8, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^8, G.3^8, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^8, G.2^2 * G.3^-1 * G.2^2 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^8, G.2^-1 * G.3 * G.2^3 * G.1^-1 * G.2^-2 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^8, G.3^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^8, G.3^2 * G.2^2 * G.1 * G.3 * G.2 * G.1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-3 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^8 ] Genus 81 action of group of order 384 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^2 * G.1 * G.3, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1^-2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 640 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.3 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^6, G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, (G.1 * G.3 * G.1^-1 * G.2^-1)^2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^6, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.2^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 480 via triangle group [ 4, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^10 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 400 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^10 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.3^2 * G.2)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, (G.1 * G.3^2 * G.2)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-3 * G.1^-1 * G.3^4 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, (G.2^-1 * G.1)^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.2^-1 * G.1)^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2 * G.1 * G.3^-1 * G.1^2 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3^3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-4 * G.1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-5 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.1^-2 * G.3^3 * G.1^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.1^-1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^12 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.3^5 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^3, (G.1 * G.3^2 * G.2)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^3, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-2 * G.1^-1 * G.3^3, (G.2 * G.3^-1)^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-5 * G.1^-1 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-2)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, (G.1 * G.3^-1)^4, (G.1 * G.3^-3)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2, G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-4 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 * G.2 * G.1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, (G.1 * G.3^2 * G.2^-1)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, (G.1 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, (G.1 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-2)^2, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^4 * G.2^-1 * G.3^-2 * G.1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2, (G.1 * G.3^-1)^4, G.2 * G.1^-1 * G.2 * G.1^-2 * G.3^2 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1^-1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^5 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.3^3 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^2 * G.2 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^6 * G.2 * G.3^-3 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^3 * G.2 * G.1^-1 * G.3^4 * G.2 * G.3^-2 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.3^6 * G.2 * G.3^-3 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^6 * G.2 * G.3^-3 * G.1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^4 * G.2 * G.3^-3 * G.1 * G.3^4 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.3 * G.2 * G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.3^3 * G.2 * G.3^-4 * G.1^-1 * G.3^3 * G.2 ] Genus 81 action of group of order 360 via triangle group [ 4, 4, 18 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-9 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-1 ] Genus 81 action of group of order 360 via triangle group [ 4, 4, 18 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3^7 * G.2 ] Genus 81 action of group of order 352 via triangle group [ 4, 4, 22 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-7 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 81 action of group of order 340 via triangle group [ 4, 4, 34 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^5 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^9 ] Genus 81 action of group of order 340 via triangle group [ 4, 4, 34 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^9 ] Genus 81 action of group of order 336 via triangle group [ 4, 4, 42 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-42 ] Genus 81 action of group of order 336 via triangle group [ 4, 4, 42 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^8 * G.2^-1 * G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 81 action of group of order 336 via triangle group [ 4, 4, 42 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-7 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 81 action of group of order 336 via triangle group [ 4, 4, 42 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^6 ] Genus 81 action of group of order 336 via triangle group [ 4, 4, 42 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-30 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 81 action of group of order 328 via triangle group [ 4, 4, 82 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-65 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 81 action of group of order 328 via triangle group [ 4, 4, 82 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^3 * G.2^-1 * G.3 * G.1^-1 * G.3^5 ] Genus 81 action of group of order 328 via triangle group [ 4, 4, 82 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^4 * G.2^-1 * G.1^2 * G.2^-1 * G.3^4 ] Genus 81 action of group of order 324 via triangle group [ 4, 4, 162 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-64 * G.1 * G.2^-1 * G.3^-16 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, (G.3^-1 * G.1)^3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.2, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3 * G.2^2 * G.1^-2 * G.3^2 * G.2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.3 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1, G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.1^-1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.1^-1 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.1^-1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2 * G.3^-2, G.2^-2 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.1^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.1^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.1^-1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1, G.2^-1 * G.3 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1, G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.2^-3 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.2^-2 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2 * G.3^-2, G.2^-3 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2^-1 * G.3^2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2^-1 * G.3^2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.3^-1 * G.2)^3, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 81 action of group of order 400 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1 ] Genus 81 action of group of order 400 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 400 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3 * G.2)^2, G.2^2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^20 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^20 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^8, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^8, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^20 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^20 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^40 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^10 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.3)^10 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^10 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^40 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^5, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1)^5, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^10 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.3 * G.1)^5, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.3 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.3 * G.1)^5, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.3 * G.1)^5 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^5, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 640 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^20 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^20 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.3 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.3 * G.1)^5, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.2 * G.1)^5, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4^3, (G.1 * G.3)^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.4^2, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^6, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.3 * G.1 * G.3 * G.1 * G.4)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 480 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.1 * G.3)^20 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.1)^5, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.4^-3 * G.2 * G.4 * G.3 * G.1^2 * G.4^-3 * G.2 * G.4^-2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.4^-1 * G.2)^5 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4^-5 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, (G.1 * G.3)^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-3 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-3 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, (G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, (G.1 * G.3)^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, (G.1 * G.3)^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^10, G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-3 * G.2 * G.4 * G.3 * G.1^2 * G.4^-3 * G.1 * G.4^-2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^10, G.4^-5 * G.2 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4^10 ] Genus 81 action of group of order 400 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^4 * G.1 * G.4 * G.3 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^6 * G.3 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^12, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^12, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.1 * G.4^5 * G.1^2 * G.4^2 * G.2 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^-12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^5 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-6 * G.1^2 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^4 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.1 * G.4^5 * G.2 * G.4 * G.1^2 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.1^2 * G.2 * G.4^-5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^2 * G.3 * G.4^-3 * G.2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.2 * G.4 * G.1^2 * G.4^3 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.4^3 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.2 * G.4^4 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-2 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4^3 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4^6 * G.3 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-3 * G.2 * G.3 * G.4^-3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.4^3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 * G.1 * G.3 * G.4^-5 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, (G.1 * G.3)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^12, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5, (G.1 * G.3)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, (G.1 * G.3)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^12, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^4 * G.1 * G.4 * G.3 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^6 * G.3 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^12, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-6 * G.1 * G.4 * G.3 * G.2 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^12, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^7 * G.3 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 * G.1 * G.3 * G.4^-5 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^6 * G.2 * G.4 * G.1^2 * G.4^3 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-5 * G.1 * G.4 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^12, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.4^3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.1 * G.4 * G.3 * G.1 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^12, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^12, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^12, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^2 * G.1 * G.4^-3 * G.2, G.4^5 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^4 * G.3 * G.4^-2 * G.1^2 * G.4^-3 * G.1 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, G.4^6 * G.1 * G.4^2 * G.3 * G.4^-3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3 * G.4^-5 * G.1 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-6 * G.2^2 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-4 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^2 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 * G.1 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^6 * G.2^2 * G.4^6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^2 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.4 * G.2 * G.4 * G.3 * G.2 * G.4^3, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^3, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^3 * G.3 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.3 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-3 * G.2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^4 * G.3 * G.1 * G.4^-5, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^12, G.4^-2 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.4 * G.1 * G.4^3 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.3)^4, G.4 * G.2 * G.4 * G.3 * G.2 * G.4^3, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.4^-3 * G.2 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-5, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^2 * G.1 * G.4^-3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, (G.2 * G.1 * G.4)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, G.4^4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.3 * G.4^-3 * G.2 * G.3 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^5 * G.1 * G.4 * G.3 * G.4^-2 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.2^2 * G.4^-6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-2 * G.1 * G.4^4 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^5 * G.1 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.1 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4^-12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^5 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.1^2 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-6 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.4^-3 * G.1 * G.4^4 * G.3 * G.4^-2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.4^-2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^6 * G.3 * G.1 * G.4^5 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.4^2 * G.3)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.2)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^5, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-2 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.1 * G.2)^6 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^12 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^18, G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^9 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-5 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-5, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4^3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-18 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^18 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-10 * G.2 * G.1 * G.4^6 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1 * G.4 * G.1^2 * G.3 * G.4^-8 * G.2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^3 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^9 * G.3 * G.2 * G.4 * G.3 * G.4^-6 * G.2 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-12 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.4^-5 * G.2 * G.1 * G.4 * G.2 * G.4^5 * G.3 * G.4^-3 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-3 * G.2 * G.4^-5 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^11 * G.3 * G.1 * G.4^5 * G.2 * G.4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^18 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-5 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2)^2, G.4^10 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-7 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-9 * G.1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 81 action of group of order 360 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^6 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^-6 * G.1 * G.4 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^-2 * G.1 * G.3 * G.4^-5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-22, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-6 * G.1 * G.3 * G.4^-4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-22 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^22 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^8 * G.3 * G.4^-1 * G.1 * G.4^-11 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-9 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^11 * G.3 * G.4^-1 * G.1 * G.2 * G.4^9 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^5 * G.3 * G.4^-6 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.1 * G.4^3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^15 * G.3 * G.1 * G.4^5 * G.2 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4^10 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-11 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-9 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-7 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^14 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.4^7 * G.3 * G.4^-3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-15 * G.1 * G.2 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-22 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-17 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.1 * G.4^5 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^9 * G.2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-3 * G.2 * G.4^9 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.3 * G.1 * G.4^2 ] Genus 81 action of group of order 352 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.4^12 * G.3 * G.1^2 * G.2 * G.4^4 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^8 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^7 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^6 * G.1 * G.4 * G.1 * G.3 * G.4^-8 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.3 * G.2 * G.4^4 * G.3 * G.1^2 * G.4^-5 * G.2 * G.3 * G.4^-2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-8 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2, G.4^10 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-4 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4^2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^11 * G.3 * G.4^-2 * G.1 * G.4^3 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-8 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^3 * G.2 * G.4^3 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2)^2, G.4^3 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4^2 * G.3 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^7 * G.2 ] Genus 81 action of group of order 340 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-10 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1^2 * G.4^-10 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-10 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-12 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-13 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-13 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^14 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^11 * G.3 * G.4^-4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-15 * G.1 * G.3 * G.4^-5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-15 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-10 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-10 * G.1 * G.2 * G.3 * G.1 * G.4^9 * G.2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-14 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-2 * G.1 * G.2 * G.4^2 * G.3 * G.4^-3 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-6 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4^6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-4 * G.2 * G.4^-2 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-6 * G.2 * G.4 * G.1 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-6 * G.2 * G.4 * G.1 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^7 * G.2 * G.4 * G.2 * G.4^6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-7 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-7 * G.1 * G.4^-4 * G.2 * G.3 * G.4^-2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^5 * G.2 * G.1 * G.4^5 * G.3 * G.4, G.4^-2 * G.2 * G.3 * G.4^-4 * G.2 * G.1^2 * G.4^5 * G.3 * G.4^-1 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6, G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.4^2 * G.1^2 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^5 * G.3 * G.4^-1, G.4^2 * G.2 * G.1 * G.4^4 * G.1^2 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-4 * G.1 * G.4 * G.2 * G.4^5, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-42 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-19 * G.2 * G.4^9 * G.3 * G.4^-1 * G.1 * G.4^-12 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-18 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.2 * G.4^-11 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^17 * G.3 * G.4^-15 * G.1 * G.2 * G.4^9 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^19 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4^12 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^33 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-23 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^16 * G.3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^37 * G.1^2 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.1 * G.2 * G.4^-11 * G.1 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-42 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-42 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^34 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-10 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-9 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-8 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^4 * G.3 * G.4^-7 * G.2 * G.1 * G.3 * G.1^2 * G.2 * G.4^8 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^35 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^29 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^4 * G.2 * G.4 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-29 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^7 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-5 * G.1 * G.4^6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-8 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-8 * G.1 * G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^13 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-6 * G.1 * G.4^7 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-28 * G.1 * G.2 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^33 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 81 action of group of order 336 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^28 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-30 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-29 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^7 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^34 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^35 * G.3 * G.1 * G.4^5 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-11 * G.1 * G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.1 * G.2 * G.4^-12 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-10 * G.1 * G.4 * G.2 * G.4^-15 * G.1 * G.2 * G.4^-11 * G.1 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-82 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-82 ] Genus 81 action of group of order 328 via quadrangle group [ 2, 2, 2, 82 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-68 * G.1 * G.2 * G.1 * G.2 * G.4^-12 ] Genus 81 action of group of order 324 via quadrangle group [ 2, 2, 2, 162 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-40 * G.2 * G.3 * G.4^-40 ] Genus 81 action of group of order 324 via quadrangle group [ 2, 2, 2, 162 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-74 * G.2 * G.4^-7 ] Genus 81 action of group of order 324 via quadrangle group [ 2, 2, 2, 162 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^69 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.2)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, (G.3 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.4^-2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, (G.3 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.3 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, (G.3 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.2 * G.3^-1 * G.4^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.2 * G.3^-1 * G.4^-1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.4^-2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.2 * G.1)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, (G.2 * G.1)^8 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, (G.4^-1 * G.2)^3, G.3^-1 * G.4 * G.3 * G.1 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.3 * G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.4 * G.3^-1 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, (G.1 * G.4 * G.3^-1 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.3^-1 * G.1)^3, G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.2 * G.3^-1 * G.4^-1 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.2 * G.3^-1 * G.4^-1 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.1 * G.3^-1)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3^-1)^2, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, (G.1 * G.3^-1)^4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, (G.1 * G.3^-1 * G.1 * G.3)^3, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2)^4, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3^-1)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.3^-1 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4, (G.1 * G.2)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.1 * G.2 * G.4^-1 * G.2)^2, G.3^-1 * G.4^-2 * G.3 * G.2 * G.4^2 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1, G.3^-1 * G.4^-2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.2 * G.3^-1 * G.4 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3^-1 * G.4 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3^-1 * G.4 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-2 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.3^-1 * G.4 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3^-1 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, (G.1 * G.3^-1)^4, G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3^-1 * G.4 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4^-1, (G.1 * G.3^-1 * G.4 * G.2)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3^-1 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, (G.2^-1 * G.3)^4, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.1 * G.2^-1)^3, (G.2^-1 * G.4^-1)^4, (G.4^-1 * G.2^-1 * G.3)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2, G.4^-2 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2^-1 * G.3)^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3)^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3)^4, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2^-1 * G.3)^4, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.1 * G.2^-1)^3, (G.1 * G.3)^4, G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.3 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.2^-1)^3, G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1, (G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1, (G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2^-1 * G.4 * G.3 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.4, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1 * G.4^-1)^3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.2^-1)^3, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.1)^4, G.3 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.2 * G.4^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.3 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.3 * G.2^-1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2^-1 * G.1)^4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.4 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2 * G.4^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.4^2 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, (G.2 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.2^-1)^3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2^-1 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, (G.2^-1 * G.1)^4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-2 * G.4 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1, (G.2^-1 * G.1)^4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, G.2^-1 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, G.2^-1 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.4, G.2^-1, G.4) ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.3)^4, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, (G.2^-1 * G.3)^4, (G.4, G.2^-1, G.4) ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, (G.2^-1 * G.3)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2^-1 * G.3)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3, G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.3)^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.3)^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.1)^4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1)^4, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.1 * G.4 * G.2^-1 * G.4^-1)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.1)^4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.4^2 * G.2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 81 action of group of order 384 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 81 has order 1536 ... group action with signature (0: +; [2,3,16]; {-}) Largest group with or without reflections for genus 81 has order 3072 ... group action with signature (0; +; [-]; {(2,3,16)}) Largest group with reflections for genus 81 has order 3072 ... group action with signature (0; +; [-]; {(2,3,16)}) Largest chiral group for genus 81 has order 1280 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 82 has order 1152 ... group action with signature (0; +; [-]; {(2,4,9)}) Check total 4291 : 2514 chiral, 1777 reflexible, with 366 non-orientable quotient actions Genus 82 actions: Genus 82 action of group of order 3888 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 3888 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 3888 via triangle group [ 2, 3, 8 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 82 action of group of order 1944 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 82 action of group of order 1944 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 82 action of group of order 1458 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^5 * G.2^-1 * G.3^-6, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 1458 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^7 * G.2 * G.3^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 82 action of group of order 1458 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.2 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-4 * G.1 * G.3 ] Genus 82 action of group of order 1458 via triangle group [ 2, 3, 18 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2, G.2 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 1296 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 1296 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 1296 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 1296 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2 * G.3^6 ] Genus 82 action of group of order 1944 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 1944 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2 * G.3^-1)^6, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 1296 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 82 action of group of order 1296 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^6, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 1296 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3 * G.2 * G.3^-1)^2, G.3^12, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3, G.3^-4 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^12, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^3, (G.2 * G.3^-3 * G.2 * G.3^-1)^2 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.2 * G.1 * G.3^2 * G.2^2 * G.3^-2 * G.1 * G.3 ] Genus 82 action of group of order 972 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3 * G.2 * G.3^-1)^2, G.3^12, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 ] Genus 82 action of group of order 720 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-4 * G.2, G.3^7 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 720 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^-5 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 82 action of group of order 664 via triangle group [ 2, 4, 166 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-38 * G.1 * G.2 * G.3^-127 ] Genus 82 action of group of order 656 via triangle group [ 2, 4, 328 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-37 * G.1 * G.2^-1 * G.3^-126 ] Genus 82 action of group of order 810 via triangle group [ 2, 5, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-2 * G.1 * G.2^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^-2 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3^2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^-2 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3^2, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-3 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-1 * G.2)^4 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^12 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 648 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 ] Genus 82 action of group of order 540 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 82 action of group of order 540 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^15 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-10 ] Genus 82 action of group of order 540 via triangle group [ 2, 6, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-14 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 82 action of group of order 540 via triangle group [ 2, 6, 30 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-13 * G.1 * G.3^3 * G.2 * G.3^-7 * G.1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 504 via triangle group [ 2, 6, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^61 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-9 * G.1 * G.3^11 ] Genus 82 action of group of order 504 via triangle group [ 2, 6, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-48 * G.1 * G.3^21 * G.2^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-6 ] Genus 82 action of group of order 504 via triangle group [ 2, 6, 84 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-12 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-6 ] Genus 82 action of group of order 492 via triangle group [ 2, 6, 246 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^67 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 82 action of group of order 648 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2^2 * G.3^-1 * G.2^3 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 82 action of group of order 648 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.2^3 * G.3^-1)^3 ] Genus 82 action of group of order 648 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.2^-1 * G.3 * G.2^4 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-9, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.2^-9, G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-5 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-5 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-5 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3 * G.2^2 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 432 via triangle group [ 2, 9, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 82 action of group of order 410 via triangle group [ 2, 10, 205 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-8 * G.1 * G.3^20 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.2 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.2^-3 * G.3^-2 * G.2^2 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.3^-3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^3 * G.2 * G.3^-2 * G.1 * G.3^6 ] Genus 82 action of group of order 432 via triangle group [ 2, 12, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 378 via triangle group [ 2, 18, 63 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^10 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 378 via triangle group [ 2, 21, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-3 * G.3^3 * G.2^-1 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-2 ] Genus 82 action of group of order 360 via triangle group [ 2, 30, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-17 * G.3^4 * G.2^-5 * G.3^4 ] Genus 82 action of group of order 360 via triangle group [ 2, 30, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.2^-1 * G.3^10 * G.2^-1 * G.3^4 * G.2^-7 * G.3 * G.2^-4 * G.3 * G.2^-1 ] Genus 82 action of group of order 360 via triangle group [ 2, 30, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^7 * G.3^-1 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 360 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-4 * G.3 * G.2^-2 * G.3 * G.2^-2 ] Genus 82 action of group of order 360 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-1 * G.3^2 * G.2^-5 * G.3 * G.2^-2 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^2 ] Genus 82 action of group of order 342 via triangle group [ 2, 57, 114 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-24 * G.2^10 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-17 ] Genus 82 action of group of order 336 via triangle group [ 2, 84, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-7 * G.2 * G.3^-1 * G.2^10 * G.3^-4 * G.2^17 * G.3^-2 ] Genus 82 action of group of order 330 via triangle group [ 2, 165, 330 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^115 * G.2^-48 * G.3 ] Genus 82 action of group of order 332 via triangle group [ 2, 166, 166 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^50 * G.3^-116 ] Genus 82 action of group of order 328 via triangle group [ 2, 328, 328 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^49 * G.3^-115 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3^2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 1944 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 972 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 82 action of group of order 972 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.1^-1 * G.3^4, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 82 action of group of order 729 via triangle group [ 3, 3, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.2 * G.1^-1 * G.3)^3, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 567 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 567 via triangle group [ 3, 3, 21 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 513 via triangle group [ 3, 3, 57 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.1 ] Genus 82 action of group of order 513 via triangle group [ 3, 3, 57 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-6 * G.1 * G.3^2 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 82 action of group of order 504 via triangle group [ 3, 3, 84 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^3 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.3^4 * G.2 * G.1 ] Genus 82 action of group of order 504 via triangle group [ 3, 3, 84 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^-5 ] Genus 82 action of group of order 972 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 82 action of group of order 972 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-2 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3^2 * G.2)^2 ] Genus 82 action of group of order 648 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 82 action of group of order 432 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-6 * G.1 * G.2^-1 * G.3^-5 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^2 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^3 * G.2 * G.1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1 * G.3 * G.2^2 * G.1^-1 * G.3^2 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-2 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, (G.2 * G.1^-1 * G.3)^3, G.2^-3 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.2^2 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 82 action of group of order 486 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.1 * G.3^2 * G.2)^2 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.1^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 82 action of group of order 432 via triangle group [ 3, 6, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 ] Genus 82 action of group of order 378 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 ] Genus 82 action of group of order 378 via triangle group [ 3, 6, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3 ] Genus 82 action of group of order 342 via triangle group [ 3, 6, 38 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.2 * G.1 * G.2^-2 * G.1 * G.3^3 ] Genus 82 action of group of order 342 via triangle group [ 3, 6, 38 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2 * G.1^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2)^3 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.2, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3^2 * G.2 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1 * G.1^-1, G.1 * G.3^-2 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2, G.1 * G.3^-1 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^2 * G.2 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 82 action of group of order 648 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2 * G.1^-1, G.1^-1 * G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 * G.2 ] Genus 82 action of group of order 360 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 82 action of group of order 360 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^4 ] Genus 82 action of group of order 360 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2, G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^3 * G.2 ] Genus 82 action of group of order 360 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 82 action of group of order 332 via triangle group [ 4, 4, 83 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-66 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-15 ] Genus 82 action of group of order 328 via triangle group [ 4, 4, 164 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-65 * G.1 * G.2^-1 * G.3^-16 ] Genus 82 action of group of order 336 via triangle group [ 4, 7, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, (G.3^-1 * G.2)^3, G.2^-7 ] Genus 82 action of group of order 336 via triangle group [ 4, 7, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1, G.2^-7 ] Genus 82 action of group of order 405 via triangle group [ 5, 5, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.1)^3, G.3^-1 * G.2 * G.1^-2 * G.2^2 * G.3^-1 ] Genus 82 action of group of order 405 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, (G.2^-1 * G.1)^3, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-2 * G.2 * G.1 * G.2^-1 ] Genus 82 action of group of order 405 via triangle group [ 5, 5, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.2)^3, G.2^2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.2 * G.4^-1)^6 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.2 * G.4^-1)^6 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, (G.1 * G.3)^6 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^6, (G.2 * G.4^-1 * G.2 * G.4)^3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 972 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^-2 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4 * G.3 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^6, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.2)^6, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1)^3, (G.3 * G.4^-1 * G.1 * G.4)^3, G.3 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^6, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.1 * G.4)^3 ] Genus 82 action of group of order 648 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^8, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.4^8, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^8, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.4^-1 * G.2)^2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^8, (G.1 * G.4 * G.3 * G.4^-1 * G.2)^2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 432 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.4^8, (G.1 * G.4 * G.3 * G.4^-1 * G.2)^2 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, (G.1 * G.3)^6, G.3 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^2 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 * G.4^3 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^5 * G.3 * G.1 * G.2 * G.4^3 * G.2 * G.4 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^5 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.1 * G.4^2 * G.2 * G.3 * G.1 * G.2 * G.4^-4 ] Genus 82 action of group of order 360 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 82 action of group of order 332 via quadrangle group [ 2, 2, 2, 83 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-41 * G.2 * G.1 * G.3 * G.4^-41 ] Genus 82 action of group of order 332 via quadrangle group [ 2, 2, 2, 83 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-76 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 82 action of group of order 332 via quadrangle group [ 2, 2, 2, 83 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-69 * G.1 * G.2 * G.1 * G.2 * G.4^-12 ] Genus 82 action of group of order 328 via quadrangle group [ 2, 2, 2, 164 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-41 * G.1 * G.4^-41 ] Genus 82 action of group of order 328 via quadrangle group [ 2, 2, 2, 164 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-75 * G.1 * G.3 * G.4^-6 ] Genus 82 action of group of order 328 via quadrangle group [ 2, 2, 2, 164 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-69 * G.1 * G.2 * G.4^-12 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^18, G.2 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1)^3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3^-1 * G.1 * G.3 * G.1)^9, G.2 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1, G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1, G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.1, G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3^-1, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.2 * G.4 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.1^2 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.4^-1 * G.2^-1)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2 * G.1)^6 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.3 * G.1 * G.2^-1 * G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.3 * G.1 * G.2^-1 * G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.3 * G.1 * G.2^-1 * G.3 * G.1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^2 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.3 * G.1)^9 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, (G.4^-1 * G.2)^3, G.3 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2^-2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.3 * G.1)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.2^-1 * G.4^-1 * G.2 * G.4^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^2 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.2^-1 * G.4^-1 * G.2 * G.4^-1)^3, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.2^-1 * G.4^-1 * G.2 * G.4^-1)^3, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, (G.4^-1 * G.2^-1)^9, G.3 * G.1^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.3 * G.1)^3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-2 * G.2^-1 * G.4, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.3)^6, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.1 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.1)^6, (G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1)^2 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 82 action of group of order 486 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.4 * G.3 ] Largest orientation-preserving group for genus 82 has order 3888 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 82 has order 7776 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 82 has order 7776 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 82 has order 3888 ... group action with signature (0: +; [2,3,8]; {-}) Largest non-orientable group for non-orientable genus 83 has order 1944 ... group action with signature (0; +; [-]; {(2,4,6)}) Check total 1539 : 1154 chiral, 385 reflexible, with 31 non-orientable quotient actions Genus 83 actions: Genus 83 action of group of order 1312 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 83 action of group of order 1312 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 83 action of group of order 1312 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 83 action of group of order 1312 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 83 action of group of order 984 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 ] Genus 83 action of group of order 984 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 83 action of group of order 672 via triangle group [ 2, 4, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-76 * G.1 * G.3 * G.2^-1 * G.3^-6 ] Genus 83 action of group of order 672 via triangle group [ 2, 4, 168 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-39 * G.1 * G.2 * G.3^-128 ] Genus 83 action of group of order 664 via triangle group [ 2, 4, 332 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-38 * G.1 * G.2^-1 * G.3^-127 ] Genus 83 action of group of order 528 via triangle group [ 2, 6, 44 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^9 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 83 action of group of order 498 via triangle group [ 2, 6, 249 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^68 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^4 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2^2 * G.1 * G.2^-3 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2^-1 * G.3 * G.2^-4 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3^3 ] Genus 83 action of group of order 656 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 83 action of group of order 480 via triangle group [ 2, 8, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-11 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 83 action of group of order 480 via triangle group [ 2, 8, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-11 * G.1 * G.3^5 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 83 action of group of order 448 via triangle group [ 2, 8, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-22 * G.1 * G.3^19 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 83 action of group of order 448 via triangle group [ 2, 8, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^36 * G.2 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.3^11 ] Genus 83 action of group of order 492 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 83 action of group of order 492 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 83 action of group of order 408 via triangle group [ 2, 12, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^21 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 83 action of group of order 384 via triangle group [ 2, 24, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-10 * G.3^-1 * G.2 * G.1, G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 83 action of group of order 384 via triangle group [ 2, 24, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 83 action of group of order 352 via triangle group [ 2, 44, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^2 * G.3^-7 * G.2 * G.3^-1 * G.2^11 * G.3^-3 * G.2 * G.3^-17 * G.2 ] Genus 83 action of group of order 352 via triangle group [ 2, 44, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-6 * G.2^12 * G.3^-4 * G.2^19 * G.3^-1 ] Genus 83 action of group of order 334 via triangle group [ 2, 167, 334 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^116 * G.2^-50 ] Genus 83 action of group of order 336 via triangle group [ 2, 168, 168 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^51 * G.3^-116 * G.2 ] Genus 83 action of group of order 336 via triangle group [ 2, 168, 168 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-50 * G.2^33 ] Genus 83 action of group of order 332 via triangle group [ 2, 332, 332 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^50 * G.3^-115 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2 ] Genus 83 action of group of order 656 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 83 action of group of order 492 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 83 action of group of order 492 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 83 action of group of order 336 via triangle group [ 4, 4, 84 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-29 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 83 action of group of order 336 via triangle group [ 4, 4, 84 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^74 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^8 ] Genus 83 action of group of order 336 via triangle group [ 4, 4, 84 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-29 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 83 action of group of order 336 via triangle group [ 4, 4, 84 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-30 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 83 action of group of order 332 via triangle group [ 4, 4, 166 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-66 * G.1 * G.2^-1 * G.3^-16 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 656 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 83 action of group of order 492 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-6 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-6 * G.2 * G.4 * G.1 * G.4^3 * G.3 * G.4^-3 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^5 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^2 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^5 * G.3 * G.1 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-2 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^5 * G.2 * G.1 * G.4^5 * G.3 * G.4, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6, G.4^-5 * G.1 * G.4^2 * G.1^2 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^5 * G.3 * G.4^-1, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.4^5 * G.2 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-4 * G.1 * G.4 * G.2 * G.4^5, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-14 * G.1 * G.4^-5 * G.1 * G.4^-9 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.4^5 * G.3 * G.4^-13 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.1^2 * G.4^-5 * G.2 * G.4^-3 * G.1 * G.3 * G.2 * G.4^-5 * G.1 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^10 * G.2 * G.4^-4 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^11 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-3 * G.2 * G.4^-8 * G.2 * G.4^-2 * G.2 * G.1 * G.4^5 * G.2 * G.4^6 * G.2 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^6 * G.2 * G.1 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^2 * G.3 * G.4^-5 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-84 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-84 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-84 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-22 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^16 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^35 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-12 * G.1 * G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.4^-13 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-21 * G.1 * G.4^-5 * G.1 * G.4^-16 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-17 * G.2 * G.4^12 * G.3 * G.1 * G.4^-12 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-18 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1^2 * G.4^-16 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^17 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.4^11 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^17 * G.3 * G.4^-15 * G.1 * G.4^5 * G.2 * G.4^4 ] Genus 83 action of group of order 336 via quadrangle group [ 2, 2, 2, 84 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^33 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 83 action of group of order 332 via quadrangle group [ 2, 2, 2, 166 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-41 * G.2 * G.3 * G.4^-41 ] Genus 83 action of group of order 332 via quadrangle group [ 2, 2, 2, 166 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-76 * G.2 * G.4^-7 ] Genus 83 action of group of order 332 via quadrangle group [ 2, 2, 2, 166 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-69 * G.1 * G.2 * G.4^-13 ] Largest orientation-preserving group for genus 83 has order 1312 ... group action with signature (0: +; [2,4,8]; {-}) Largest group with or without reflections for genus 83 has order 1344 ... group action with signature (0; +; [-]; {(2,4,168)}) Largest group with reflections for genus 83 has order 1344 ... group action with signature (0; +; [-]; {(2,4,168)}) Largest chiral group for genus 83 has order 1312 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 84 has order 656 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 386 : 304 chiral, 82 reflexible, with 35 non-orientable quotient actions Genus 84 actions: Genus 84 action of group of order 696 via triangle group [ 2, 4, 87 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-68 * G.1 * G.3^11 * G.2^-1 * G.3^-7 ] Genus 84 action of group of order 680 via triangle group [ 2, 4, 170 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-40 * G.1 * G.2 * G.3^-129 ] Genus 84 action of group of order 672 via triangle group [ 2, 4, 336 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-39 * G.1 * G.2^-1 * G.3^-128 ] Genus 84 action of group of order 516 via triangle group [ 2, 6, 86 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^63 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-9 * G.1 * G.3^11 ] Genus 84 action of group of order 464 via triangle group [ 2, 8, 58 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-24 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-17 ] Genus 84 action of group of order 440 via triangle group [ 2, 10, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^22 * G.2 * G.1 * G.3 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^6 ] Genus 84 action of group of order 420 via triangle group [ 2, 10, 210 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^27 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^3 ] Genus 84 action of group of order 408 via triangle group [ 2, 12, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.1 * G.3^16 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 * G.2^-1 ] Genus 84 action of group of order 420 via triangle group [ 2, 14, 30 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^-7 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-7 ] Genus 84 action of group of order 416 via triangle group [ 2, 16, 26 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-5 ] Genus 84 action of group of order 364 via triangle group [ 2, 26, 182 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-13 * G.3^4 * G.2^-5 * G.3^4 ] Genus 84 action of group of order 360 via triangle group [ 2, 36, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-4 * G.3^4 * G.2^-4 * G.3^4 ] Genus 84 action of group of order 352 via triangle group [ 2, 44, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-9 * G.3^4 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 84 action of group of order 350 via triangle group [ 2, 50, 175 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-12 * G.3^4 * G.2^-6 * G.3^3 ] Genus 84 action of group of order 348 via triangle group [ 2, 58, 174 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-24 * G.2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^20 ] Genus 84 action of group of order 344 via triangle group [ 2, 86, 172 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-52 * G.2^33 ] Genus 84 action of group of order 348 via triangle group [ 2, 87, 87 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-83 * G.3 * G.2^-1 ] Genus 84 action of group of order 338 via triangle group [ 2, 169, 338 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^117 * G.2^-50 * G.3 ] Genus 84 action of group of order 340 via triangle group [ 2, 170, 170 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^52 * G.3^-118 ] Genus 84 action of group of order 336 via triangle group [ 2, 336, 336 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^51 * G.3^-117 ] Genus 84 action of group of order 516 via triangle group [ 3, 3, 86 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-6 * G.1 * G.3^2 * G.2 * G.3^-5 ] Genus 84 action of group of order 516 via triangle group [ 3, 3, 86 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-9 ] Genus 84 action of group of order 507 via triangle group [ 3, 3, 169 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 84 action of group of order 507 via triangle group [ 3, 3, 169 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-4 * G.1^-1 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^68 * G.2 * G.1 * G.3^16 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-6 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.2 * G.3^-5 * G.1 * G.3^-4 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-2 * G.3^-4 * G.1 * G.3^-1 * G.1 * G.3^3 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1 * G.3^2 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.2^-1 * G.3^-1 * G.1 * G.3^-4 * G.1 * G.2^-1 * G.3^4 ] Genus 84 action of group of order 340 via triangle group [ 4, 4, 85 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-3 * G.2 * G.3^-6 * G.1 * G.3^-3 ] Genus 84 action of group of order 336 via triangle group [ 4, 4, 168 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^74 * G.2 * G.1^-1 * G.3^9 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^5 * G.1 * G.4^-5, G.4^-8 * G.2 * G.3 * G.1 * G.4^-8 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.2 * G.4^10 * G.1 * G.3 * G.4^-6 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^5)^2, G.4^-2 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-7 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.4^6 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^11 * G.1^2 * G.4^4 * G.2 * G.4 * G.2 * G.4 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-42 * G.2 * G.1 * G.3 * G.4^-42 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-78 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 84 action of group of order 340 via quadrangle group [ 2, 2, 2, 85 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^71 * G.2 * G.1 * G.2 * G.1 * G.4^12 ] Genus 84 action of group of order 336 via quadrangle group [ 2, 2, 2, 168 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-42 * G.1 * G.4^-42 ] Genus 84 action of group of order 336 via quadrangle group [ 2, 2, 2, 168 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-77 * G.1 * G.3 * G.4^-6 ] Genus 84 action of group of order 336 via quadrangle group [ 2, 2, 2, 168 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-71 * G.1 * G.2 * G.4^-12 ] Largest orientation-preserving group for genus 84 has order 696 ... group action with signature (0: +; [2,4,87]; {-}) Largest group with or without reflections for genus 84 has order 1392 ... group action with signature (0; +; [-]; {(2,4,87)}) Largest group with reflections for genus 84 has order 1392 ... group action with signature (0; +; [-]; {(2,4,87)}) No chiral group action for genus 84 Largest non-orientable group for non-orientable genus 85 has order 696 ... group action with signature (0; +; [-]; {(2,4,87)}) Check total 46 : 0 chiral, 46 reflexible, with 14 non-orientable quotient actions Genus 85 actions: Genus 85 action of group of order 4032 via triangle group [ 2, 3, 8 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^3, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 4032 via triangle group [ 2, 3, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-2 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 85 action of group of order 2016 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 2016 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 1440 via triangle group [ 2, 3, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.3^6, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 85 action of group of order 1152 via triangle group [ 2, 3, 48 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-6 * G.1 * G.3^6 * G.2 * G.3^-7 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 85 action of group of order 1152 via triangle group [ 2, 3, 48 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^5 ] Genus 85 action of group of order 2016 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.2^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-1)^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-1)^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 85 action of group of order 1344 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 85 action of group of order 800 via triangle group [ 2, 4, 25 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2, G.3^-7 * G.1 * G.3^10 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 85 action of group of order 784 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^7 * G.2^-1 * G.3 * G.2^-2 * G.3^-7 * G.2 ] Genus 85 action of group of order 720 via triangle group [ 2, 4, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2 * G.3^-1)^6, G.3^7 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 85 action of group of order 704 via triangle group [ 2, 4, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-25 * G.1 * G.3^11 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 85 action of group of order 704 via triangle group [ 2, 4, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-70 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.3^-8 ] Genus 85 action of group of order 688 via triangle group [ 2, 4, 172 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2 * G.3^-130 ] Genus 85 action of group of order 680 via triangle group [ 2, 4, 340 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-40 * G.1 * G.2^-1 * G.3^-129 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-4 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 85 action of group of order 1008 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 720 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^10, G.3^2 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 720 via triangle group [ 2, 6, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1)^4, (G.2 * G.3^-3 * G.2)^2, G.3^10 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 672 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 630 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 85 action of group of order 630 via triangle group [ 2, 6, 15 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3^6 * G.2^2 * G.1 * G.3^5 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^6 * G.2^2 * G.1 * G.3^5 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^4 * G.2 * G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-2 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, G.3^4 * G.2^-2 * G.3^-2 * G.1 * G.2^-1 * G.3 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^3 * G.2 * G.3^-2 * G.1 * G.3^6 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^4 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.3^2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-5 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.1 * G.3^5 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 576 via triangle group [ 2, 6, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-7 * G.1 * G.3^7 * G.2^-1 * G.3^-9 ] Genus 85 action of group of order 546 via triangle group [ 2, 6, 39 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 546 via triangle group [ 2, 6, 39 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 85 action of group of order 528 via triangle group [ 2, 6, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3 * G.2 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 522 via triangle group [ 2, 6, 87 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^71 * G.2 * G.3^-8 * G.1 * G.3^7 ] Genus 85 action of group of order 510 via triangle group [ 2, 6, 255 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-49 * G.1 * G.3^21 * G.2^-1 * G.1 * G.2^-1 * G.3^-13 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^8 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2, (G.2^3 * G.3^-1)^3 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, G.3^8, G.1 * G.3^2 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.3^2 * G.2^-4 * G.3^-2 * G.2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.1 * G.2^-3 * G.3^2 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, (G.2 * G.3^-2 * G.2^2)^2, (G.2 * G.3^-3 * G.2)^2 ] Genus 85 action of group of order 576 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.3^12 ] Genus 85 action of group of order 576 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^12 ] Genus 85 action of group of order 504 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 504 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 480 via triangle group [ 2, 10, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.2 * G.3^-1 * G.1 * G.2^-3 * G.3^-2 * G.2 * G.3^-2 ] Genus 85 action of group of order 480 via triangle group [ 2, 10, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^10 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 85 action of group of order 504 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.2^-5 * G.3^-5, G.2^12 ] Genus 85 action of group of order 480 via triangle group [ 2, 12, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3 * G.2^-4 * G.3^4, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^3 * G.2^3 * G.3^-1 * G.2^2 * G.1 ] Genus 85 action of group of order 432 via triangle group [ 2, 12, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^2 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 ] Genus 85 action of group of order 432 via triangle group [ 2, 12, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 432 via triangle group [ 2, 12, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^21 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 85 action of group of order 432 via triangle group [ 2, 12, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^8 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3^19 ] Genus 85 action of group of order 408 via triangle group [ 2, 12, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-2 * G.1 * G.3^14 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 432 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-5 * G.3^3 * G.2^-1 * G.3 ] Genus 85 action of group of order 432 via triangle group [ 2, 18, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^-1 * G.3^4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 374 via triangle group [ 2, 22, 187 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^9 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-4 * G.3^-1 * G.2^4 * G.1 * G.2^-4 * G.3^-1 * G.2^2 * G.1, G.2^-3 * G.3^2 * G.2^-1 * G.3^4 * G.2^-7 * G.3 * G.2^-4 * G.3 * G.2^-1 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^4 * G.2^-15 * G.3^2 * G.2^-1 * G.3^2 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-9 * G.3^3 * G.2^-1 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-11 * G.3^4 * G.2^-5 * G.3^4 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-3 * G.2^4 * G.3^-5 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-2 * G.2^2 * G.3^-1 * G.2^2 * G.3^-5 ] Genus 85 action of group of order 384 via triangle group [ 2, 24, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 85 action of group of order 400 via triangle group [ 2, 25, 25 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.2^-1 * G.3 * G.2^-1 * G.3^7 * G.2^-1 * G.3^3 * G.2^-8 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 378 via triangle group [ 2, 27, 54 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3 * G.2^-4 * G.3^4 * G.2^-1 * G.3 * G.2^-10 * G.3^4 ] Genus 85 action of group of order 378 via triangle group [ 2, 27, 54 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-2 * G.3^3 * G.2^-2 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-7 * G.3^4 ] Genus 85 action of group of order 392 via triangle group [ 2, 28, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.1 * G.2^-4 * G.3 * G.2^5 * G.1 * G.2^-1 * G.3 * G.2, G.2^-5 * G.3^4 * G.2^-1 * G.3^4 * G.2^-4 * G.3 * G.2^-2 * G.3 * G.2^-6 ] Genus 85 action of group of order 392 via triangle group [ 2, 28, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-15 * G.3^4 * G.2^-5 * G.3^4 ] Genus 85 action of group of order 392 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 360 via triangle group [ 2, 36, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^-2 * G.2^10 * G.3^-4 * G.2^16 * G.3^-4 ] Genus 85 action of group of order 360 via triangle group [ 2, 45, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-45 ] Genus 85 action of group of order 360 via triangle group [ 2, 60, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-25 * G.2^2 * G.3^-1 * G.2^10 * G.3^-4 * G.2 * G.3^-14 * G.2^2 ] Genus 85 action of group of order 360 via triangle group [ 2, 60, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-25 * G.2^13 * G.3^-2 * G.2^19 * G.3^-1 ] Genus 85 action of group of order 360 via triangle group [ 2, 60, 60 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-5 * G.3^4 * G.2^-5 * G.3^4 * G.2^-2 ] Genus 85 action of group of order 352 via triangle group [ 2, 88, 88 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-53 * G.2^33 * G.3^-1 ] Genus 85 action of group of order 352 via triangle group [ 2, 88, 88 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-27 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 85 action of group of order 342 via triangle group [ 2, 171, 342 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^118 * G.2^-52 ] Genus 85 action of group of order 344 via triangle group [ 2, 172, 172 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^53 * G.3^-118 * G.2 ] Genus 85 action of group of order 340 via triangle group [ 2, 340, 340 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^52 * G.3^-117 * G.2 ] Genus 85 action of group of order 2016 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, (G.2^-1 * G.3^-1 * G.1 * G.3)^3, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 2016 via triangle group [ 3, 3, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 1008 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 85 action of group of order 1008 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 85 action of group of order 720 via triangle group [ 3, 3, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3^2 * G.2)^2, (G.1^-1 * G.3 * G.2^-1 * G.3^-1)^2, G.3^10 ] Genus 85 action of group of order 576 via triangle group [ 3, 3, 24 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^4 ] Genus 85 action of group of order 576 via triangle group [ 3, 3, 24 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 85 action of group of order 1008 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-2 ] Genus 85 action of group of order 672 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 576 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 85 action of group of order 576 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.3^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 576 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 85 action of group of order 576 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.3^-1)^4, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 85 action of group of order 576 via triangle group [ 3, 4, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, (G.2 * G.3^-1)^4 ] Genus 85 action of group of order 504 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3^2 * G.2 * G.3^-2 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^2 * G.2^2 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.2^-2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2^2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3)^2 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3^2 * G.2, G.3 * G.2^-1 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^2 * G.2^2 * G.1 * G.3^2 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.1 * G.3^2 * G.2, G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3^2 * G.2, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1, G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 360 via triangle group [ 3, 6, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 85 action of group of order 360 via triangle group [ 3, 6, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 85 action of group of order 360 via triangle group [ 3, 6, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 85 action of group of order 360 via triangle group [ 3, 6, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.1 * G.3^3 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 85 action of group of order 360 via triangle group [ 3, 6, 30 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, (G.1 * G.3^3 * G.2^-1)^2 ] Genus 85 action of group of order 342 via triangle group [ 3, 6, 114 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 85 action of group of order 342 via triangle group [ 3, 6, 114 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 85 action of group of order 360 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-3 * G.1 * G.2^-2 * G.3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3, (G.1 * G.3 * G.2^2)^2 ] Genus 85 action of group of order 360 via triangle group [ 3, 10, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^10, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1^-1 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2)^3 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2, (G.1 * G.3 * G.2^-1 * G.1 * G.2^-1)^2 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, G.1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 672 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 85 action of group of order 392 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.2 * G.3^-5 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 ] Genus 85 action of group of order 360 via triangle group [ 4, 4, 30 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.3^3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 85 action of group of order 360 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^5 * G.2^-2 * G.3^-2 * G.1 * G.3^-2 * G.1 * G.3 ] Genus 85 action of group of order 360 via triangle group [ 4, 4, 30 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 85 action of group of order 352 via triangle group [ 4, 4, 44 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-33 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 85 action of group of order 352 via triangle group [ 4, 4, 44 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^44 ] Genus 85 action of group of order 352 via triangle group [ 4, 4, 44 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-6 * G.1 ] Genus 85 action of group of order 352 via triangle group [ 4, 4, 44 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^-6 * G.1^-1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 85 action of group of order 344 via triangle group [ 4, 4, 86 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^69 * G.2 * G.1 * G.3^16 ] Genus 85 action of group of order 340 via triangle group [ 4, 4, 170 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^68 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^11 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^2 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.3 * G.2 * G.1)^2 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^6 ] Genus 85 action of group of order 360 via triangle group [ 5, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^-5, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2^2 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.2 * G.4^-1)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, (G.2 * G.4^-1)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^6, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^6, (G.2 * G.4^-1)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^6, G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^6, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^8, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.3 * G.4^-1 * G.2 * G.4)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, (G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^7, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, (G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1 * G.1 * G.4)^3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^9, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 1008 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^42 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^14 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^42 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^14 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^42 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^14 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.3 * G.1)^21 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^8, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, (G.1 * G.2)^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1 * G.4)^3, (G.1 * G.2)^6 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1 * G.4)^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1 * G.4)^3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^8, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^7, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 672 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.3 * G.1)^21 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^42 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-3 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^14 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^14 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^14 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^14 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^14 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 448 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, (G.1 * G.2)^6, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-9, G.1 * G.4 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-9, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-9, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 432 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 420 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.1 * G.4^6, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.4^-1 * G.2)^7 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^14, (G.3 * G.1)^7 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, (G.1 * G.3)^14 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^7 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^6 * G.3 * G.1 * G.4^-7 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.3 * G.1)^7 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^2 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^5 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^6 * G.3 * G.1 * G.3 * G.4^-6, G.2 * G.4^6 * G.3 * G.1 * G.4^-7 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^5 * G.3 * G.4^-2 * G.2 * G.4^4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^14, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^6 * G.1 * G.3 * G.4^-6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.4^2, G.4 * G.3 * G.4^-2 * G.2 * G.4^-4 * G.2 * G.1 * G.4^4 * G.2 * G.4^2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^14, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3)^2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4^7 * G.1^2 * G.3 * G.1 * G.3 * G.4^-5, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^8 * G.3 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 392 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^7 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-5 * G.1 * G.4^5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-2 * G.1 * G.4^2, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^7 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-7 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^16, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.4 * G.3 * G.4^-7, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-5 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.1^2 * G.4^6 * G.3 * G.4^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^16, G.1 * G.4^-3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-5 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.4 * G.3 * G.4^-7, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-5 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-5 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-5, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.4^3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, (G.1 * G.2)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, (G.1 * G.2)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, (G.1 * G.2)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, (G.1 * G.3)^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-8 * G.2 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-6 * G.1 * G.2 * G.1^2 * G.3 * G.4^-9 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^16, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^16, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^16, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 * G.4^-1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-8 * G.2 * G.1 * G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^16, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^16, G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^16, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 384 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-3 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.4^-6 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4^7, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4^4 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^7 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.3 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^6 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4^7 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.4^-5 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-6 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4^5 * G.1^2 * G.2 * G.4^-5 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 364 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^6 * G.2 * G.4^-5, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.4^-6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4^7, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^6 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.4^9 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^9 * G.3 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-11 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^7 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^7 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-6 * G.1 * G.3 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.1 * G.2 * G.4^-1 * G.1^2 * G.3 * G.4^-4 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^7 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^8 * G.2 * G.4^-5, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3)^4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^3 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^3 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, (G.1 * G.3)^6, G.4^5 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.4^2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-30 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-7 * G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-12 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^18 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.2 * G.4 * G.3 * G.4^-17 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^7 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^16 * G.1 * G.4 * G.3 * G.4^-12 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-30 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^12 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^10 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-9 * G.2 * G.4^-5 * G.1 * G.2 * G.4^2 * G.2 * G.4^8 * G.2 * G.4 * G.2 * G.4^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^24 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^6 * G.3 * G.4^-7 * G.1 * G.2 * G.4^16 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^30 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-8 * G.1 * G.4^6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^5 * G.2 * G.4^-6 * G.3 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-21 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-3 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^14 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^9 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^12 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^3 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-14 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-44 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^29 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-12 * G.2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^26 * G.3 * G.1 * G.3 * G.1^2 * G.4^-9 * G.1 * G.4^7 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^18 * G.2 * G.3 * G.4^-12 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^44 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^36 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-3 * G.2 * G.4^8 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-3 * G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.4 * G.2 * G.4^9 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.1 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^6 * G.2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.1 * G.4^3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.1 * G.2 * G.4^-7 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^9 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-12 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-7 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^13 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^9 * G.1 * G.4 * G.1^2 * G.3 * G.4^-11 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^-5 * G.1 * G.4^5 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^11 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4^3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-9 * G.1 * G.4 * G.1^2 * G.2 * G.1 * G.4^10 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4^2 * G.3 * G.4 * G.3 * G.4^7 * G.3 * G.1^2 * G.2 * G.4^-5 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.4^8 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^8 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^7 * G.3 * G.4^-7 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-6 * G.1 * G.4^5 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^6 * G.2 * G.4^-2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^9 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-16 * G.2 * G.4 * G.3 * G.4^-18 * G.2 * G.4^6 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-38 * G.2 * G.1 * G.4^5 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-12 * G.1 * G.4 * G.2 * G.4^-28 * G.1 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-4 * G.2 * G.4^3 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.4^3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^6 * G.2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.4^-17 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4 * G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^7 * G.3 * G.4^-3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-16 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^15 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-2 ] Genus 85 action of group of order 352 via quadrangle group [ 2, 2, 2, 44 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^17 * G.2 * G.4^-1 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^18 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^11 * G.3 * G.4^-15 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-8 * G.2 * G.4 * G.1^2 * G.4^19 * G.3 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-14 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-13 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-24 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^4 * G.3 * G.4^-3 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.4^15 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-23 * G.1 * G.3 * G.4^-5 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-3 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-15 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^17 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-15 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4^3 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.4^-11 * G.1 * G.4 * G.1^2 * G.4^12 ] Genus 85 action of group of order 348 via quadrangle group [ 2, 2, 2, 58 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^11 * G.2 * G.1 * G.4^17 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-15 * G.2 * G.4 * G.3 * G.4^-17 * G.1 * G.4^-1 * G.2 * G.4^6 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-16 * G.2 * G.4 * G.3 * G.4^-17 * G.1 * G.4^-1 * G.2 * G.4^6 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-38 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^37 * G.3 * G.1 * G.4^5 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-12 * G.1 * G.4 * G.2 * G.4^-15 * G.1 * G.2 * G.4^-12 * G.1 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-11 * G.1 * G.4 * G.2 * G.4^-15 * G.1 * G.2 * G.4^-12 * G.1 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-86 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-86 ] Genus 85 action of group of order 344 via quadrangle group [ 2, 2, 2, 86 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^72 * G.2 * G.1 * G.2 * G.1 * G.4^12 ] Genus 85 action of group of order 340 via quadrangle group [ 2, 2, 2, 170 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-42 * G.2 * G.3 * G.4^-42 ] Genus 85 action of group of order 340 via quadrangle group [ 2, 2, 2, 170 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-78 * G.2 * G.4^-7 ] Genus 85 action of group of order 340 via quadrangle group [ 2, 2, 2, 170 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^72 * G.1^2 * G.2 * G.1 * G.4^12 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^9, (G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.1 * G.3^-1)^7, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.3, (G.1 * G.3 * G.4^-1 * G.1 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.3^-1)^2, (G.3 * G.1 * G.4)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.2 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.3 * G.2 * G.4)^3, (G.2 * G.4 * G.2 * G.4^-1 * G.3)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3^-1 * G.4 * G.3 * G.1 * G.4 * G.3^-1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.3 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^12, (G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1)^3, G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.3^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^12, (G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.1^2 * G.2 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4 * G.3 * G.1 * G.3^-1 * G.1^2 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.4 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2^2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1)^4, (G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.3^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.2)^3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.1 * G.2)^4, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.3^-1 * G.1)^3, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.3 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.3 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.2 * G.1)^3, G.4^-5, (G.3 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3 * G.4^-2)^2, G.4^-5, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, (G.3 * G.4^-2)^2, G.4^-5, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.3 * G.4^-2)^2, G.4^-5, G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-5, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4^-5, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.3 * G.4^-2)^2, G.4^-5, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.4^-5, G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3^-1 * G.1)^3, (G.2 * G.4 * G.3)^2, G.4^-5, G.4^-2 * G.3 * G.1 * G.4^2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3 * G.4^-2)^2, G.4^-5, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.3 * G.4^-2)^2, G.4^-5, G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-2 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.3)^3, G.4^-5, G.3^-1 * G.4^-2 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.4^-5, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.3^-1 * G.1)^3, G.4^-5, (G.1 * G.2)^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.4^-1 * G.3)^3, G.4^-5, (G.1 * G.2)^4, G.3^-1 * G.4^-2 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-5, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.4^-1 * G.2)^3, G.4^-5, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.4^-1 * G.3)^3, G.4^-5, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-5, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.2 * G.4^2 * G.2 * G.1 * G.3^-1 * G.4^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4, G.4 * G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.3^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.3 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4^-1)^2, G.4^-5, G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^2 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4^-5, (G.2 * G.4^2 * G.3)^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.2 * G.1)^3, G.4^-5, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-5, (G.1 * G.4^2 * G.3)^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-5, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, (G.4^-1 * G.3)^3, G.4^-5, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-5, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-5, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-5, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4 * G.3 * G.1 * G.4 * G.2, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-5, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.4^2, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.4^-5, G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.4^-5, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 2, 3, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-5, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.4^-2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.4 * G.3 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, (G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1)^2, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1, (G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1 * G.2^-1 * G.3 * G.1)^3, G.3 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, (G.1 * G.2^-1 * G.3)^3, G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1 * G.2^-1 * G.3 * G.1)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.4^-1 * G.2 * G.4^-1)^3, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, G.3 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.1 * G.2^-1 * G.3)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2)^3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3)^2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.4, (G.2^-1 * G.4^-1)^4, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, (G.1 * G.3)^4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, (G.2^-1 * G.4^-1)^4, G.4 * G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.4 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, (G.3 * G.1)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, (G.2^-1 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, (G.2^-1 * G.4^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, (G.1 * G.3)^4, G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 85 action of group of order 504 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^4, (G.2, G.4)^3, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1 * G.4 * G.2, G.3 * G.1^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, (G.2^-1 * G.3)^4, (G.2^-1 * G.4^-1)^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2^-1)^3, G.4^-5, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.3 * G.2^-1)^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, (G.2^-1 * G.3)^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.2^-1 * G.3 * G.2^-1 * G.4^-2 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-5, (G.2^-1 * G.4^-1)^4, (G.3 * G.2^-1)^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, G.4^-5, G.4^-2 * G.1 * G.2^-1 * G.4^2 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.2^-1)^3, (G.3 * G.1)^3, G.4^-5, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1)^4, G.2 * G.4^-2 * G.2^-1 * G.1 * G.2^-1 * G.4^2 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-5, G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, G.4^-5, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.2^-1)^3, (G.4^-1 * G.2^-1)^3, G.4^-5, G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.4^-5, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-5, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, (G.3 * G.2^-1)^3, (G.3 * G.1)^3, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-2 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-5, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1)^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, G.4^-5, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^2 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-5, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, (G.1 * G.2^-1)^5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.4^-5, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-5, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.4^-1 * G.2^-1)^3, (G.2 * G.4^-2)^2, G.4^-5, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-5, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2^-1)^3, G.4^-5, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-5, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4, G.4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-5, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-5, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-5, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-5, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, G.4^-5, G.2 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-5, G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-5, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-5, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-5, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.4^-5, G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-5, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1, (G.4^-1 * G.2^-1)^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1, G.4^-5 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.3 * G.1)^3 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.2 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.4^-5, G.2 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-2 ] Genus 85 action of group of order 360 via quadrangle group [ 2, 3, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-5, G.3 * G.4^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Largest orientation-preserving group for genus 85 has order 4032 ... group action with signature (0: +; [2,3,8]; {-}) Largest group with or without reflections for genus 85 has order 8064 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest group with reflections for genus 85 has order 8064 ... group action with signature (0; +; [-]; {(2,3,8)}) Largest chiral group for genus 85 has order 2016 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 86 has order 4032 ... group action with signature (0; +; [-]; {(2,3,8)}) Check total 3355 : 2536 chiral, 819 reflexible, with 259 non-orientable quotient actions Genus 86 actions: Genus 86 action of group of order 1200 via triangle group [ 2, 3, 40 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.3^10 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^5 ] Genus 86 action of group of order 696 via triangle group [ 2, 4, 174 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-174 ] Genus 86 action of group of order 688 via triangle group [ 2, 4, 344 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2^-1 * G.3^-130 ] Genus 86 action of group of order 600 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-3 ] Genus 86 action of group of order 600 via triangle group [ 2, 6, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 86 action of group of order 528 via triangle group [ 2, 6, 88 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-63 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-17 ] Genus 86 action of group of order 516 via triangle group [ 2, 6, 258 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-47 * G.1 * G.3 * G.2 * G.1 * G.3^22 * G.2^-1 * G.1 * G.2^-1 * G.3^-13 ] Genus 86 action of group of order 464 via triangle group [ 2, 8, 116 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-24 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-19 ] Genus 86 action of group of order 450 via triangle group [ 2, 10, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-7 * G.1 * G.3^22 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 86 action of group of order 430 via triangle group [ 2, 10, 215 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^8 * G.2 * G.3^-3 * G.1 * G.3^21 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 86 action of group of order 400 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.3^-2 * G.2^8 ] Genus 86 action of group of order 400 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-8 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^9 * G.2 * G.3^-4 * G.1 * G.3^6 ] Genus 86 action of group of order 400 via triangle group [ 2, 20, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-2 * G.3 * G.2^10 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.2^-1 * G.3^-3 ] Genus 86 action of group of order 408 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.3^-1 * G.2^6 * G.3^-4 * G.2 ] Genus 86 action of group of order 408 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.3^-1 * G.2^6 * G.3^-1 * G.2^3 * G.3^-1 ] Genus 86 action of group of order 408 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.3^-1 * G.2^6 * G.3^-1 * G.2 * G.3^-3 ] Genus 86 action of group of order 408 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.3^-1 * G.2^6 * G.3^-2 * G.2^3 ] Genus 86 action of group of order 346 via triangle group [ 2, 173, 346 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^119 * G.2^-52 * G.3 ] Genus 86 action of group of order 348 via triangle group [ 2, 174, 174 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^54 * G.3^-120 ] Genus 86 action of group of order 344 via triangle group [ 2, 344, 344 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^53 * G.3^-119 ] Genus 86 action of group of order 600 via triangle group [ 3, 3, 20 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^4 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 86 action of group of order 348 via triangle group [ 4, 4, 87 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^87 ] Genus 86 action of group of order 348 via triangle group [ 4, 4, 87 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3^-1 * G.1 * G.3^-2 * G.2 * G.3^-3 ] Genus 86 action of group of order 348 via triangle group [ 4, 4, 87 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3^-2 * G.2 * G.3^-1 * G.1 * G.3^-3 ] Genus 86 action of group of order 344 via triangle group [ 4, 4, 172 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^69 * G.2 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^11 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-14 * G.2 * G.3 * G.1 * G.4^-14 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-3 * G.2 * G.4^13 * G.3 * G.1 * G.4^-12 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.1 * G.4^4 * G.2 * G.3 * G.1 * G.4^3 * G.2 * G.4^5 * G.1^2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.4^-13 * G.1 * G.2 * G.1 * G.4^12 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-8 * G.2 * G.4^-2 * G.2 * G.1 * G.4^5 * G.2 * G.4^6 * G.2 * G.4 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-4 * G.1 * G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^6 * G.2 * G.1 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-43 * G.2 * G.1 * G.3 * G.4^-43 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-80 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 86 action of group of order 348 via quadrangle group [ 2, 2, 2, 87 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^73 * G.2 * G.1 * G.2 * G.1 * G.4^12 ] Genus 86 action of group of order 344 via quadrangle group [ 2, 2, 2, 172 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-43 * G.1 * G.4^-43 ] Genus 86 action of group of order 344 via quadrangle group [ 2, 2, 2, 172 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-79 * G.1 * G.3 * G.4^-6 ] Genus 86 action of group of order 344 via quadrangle group [ 2, 2, 2, 172 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^73 * G.1^2 * G.2 * G.1 * G.4^12 ] Largest orientation-preserving group for genus 86 has order 1200 ... group action with signature (0: +; [2,3,40]; {-}) Largest group with or without reflections for genus 86 has order 2400 ... group action with signature (0; +; [-]; {(2,3,40)}) Largest group with reflections for genus 86 has order 2400 ... group action with signature (0; +; [-]; {(2,3,40)}) Largest chiral group for genus 86 has order 408 ... group action with signature (0: +; [2,24,24]; {-}) Largest non-orientable group for non-orientable genus 87 has order 348 ... group action with signature (0; +; [-]; {(2,2,2,87)}) Check total 37 : 4 chiral, 33 reflexible, with 6 non-orientable quotient actions Genus 87 actions: Genus 87 action of group of order 2064 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 87 action of group of order 2064 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 87 action of group of order 720 via triangle group [ 2, 4, 90 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-71 * G.1 * G.3^11 * G.2^-1 * G.3^-7 ] Genus 87 action of group of order 704 via triangle group [ 2, 4, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-70 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 87 action of group of order 704 via triangle group [ 2, 4, 176 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-176 ] Genus 87 action of group of order 696 via triangle group [ 2, 4, 348 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-39 * G.1 * G.2^-1 * G.3^-134 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3 * G.2 * G.3^-1 * G.2^3 * G.3^-3 * G.1 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 87 action of group of order 602 via triangle group [ 2, 7, 14 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 ] Genus 87 action of group of order 480 via triangle group [ 2, 8, 60 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-9 * G.1 * G.3^2 * G.2 * G.1 * G.3^6 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 87 action of group of order 480 via triangle group [ 2, 8, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-20 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 87 action of group of order 480 via triangle group [ 2, 8, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-46 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-5 ] Genus 87 action of group of order 480 via triangle group [ 2, 8, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-24 * G.1 * G.3^21 * G.2 * G.3^-8 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 87 action of group of order 464 via triangle group [ 2, 8, 232 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-23 * G.1 * G.3^20 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 87 action of group of order 464 via triangle group [ 2, 8, 232 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-23 * G.1 * G.3^20 * G.2 * G.3^-8 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 87 action of group of order 406 via triangle group [ 2, 14, 203 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-2 * G.3^4 * G.2^-1)^2, G.3^15 * G.2 * G.3^-3 * G.1 * G.3^10 ] Genus 87 action of group of order 384 via triangle group [ 2, 24, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^9 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 87 action of group of order 384 via triangle group [ 2, 24, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 87 action of group of order 360 via triangle group [ 2, 90, 90 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-86 * G.3 * G.2^-1 ] Genus 87 action of group of order 354 via triangle group [ 2, 118, 177 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-23 * G.2^13 * G.3^-2 * G.2^20 ] Genus 87 action of group of order 350 via triangle group [ 2, 175, 350 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^120 * G.2^-54 ] Genus 87 action of group of order 352 via triangle group [ 2, 176, 176 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^55 * G.3^-120 * G.2 ] Genus 87 action of group of order 352 via triangle group [ 2, 176, 176 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-54 * G.2^34 ] Genus 87 action of group of order 348 via triangle group [ 2, 348, 348 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^54 * G.3^-119 * G.2 ] Genus 87 action of group of order 1032 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 87 action of group of order 1032 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 87 action of group of order 516 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 87 action of group of order 516 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 87 action of group of order 360 via triangle group [ 4, 4, 45 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^29 * G.2 * G.3^-5 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-7 * G.1 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-33 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^39 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^88 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-32 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-32 * G.1^-1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 87 action of group of order 352 via triangle group [ 4, 4, 88 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-6 * G.1 ] Genus 87 action of group of order 348 via triangle group [ 4, 4, 174 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^74 * G.2 * G.1^-1 * G.3^12 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 688 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 87 action of group of order 516 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-22 * G.2 * G.1 * G.3 * G.4^-22 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-39 * G.1^2 * G.4^-6 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^37 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^45 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^32 * G.3 * G.4^-6 * G.2 * G.1 * G.4^6 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-32 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-35 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^32 * G.2 * G.3 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 87 action of group of order 360 via quadrangle group [ 2, 2, 2, 45 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^45 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-88 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-88 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-88 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-17 * G.2 * G.4 * G.3 * G.4^-18 * G.2 * G.4^6 * G.3 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^33 * G.3 * G.4^-5 * G.2 * G.1 * G.4^5 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-13 * G.1 * G.4 * G.2 * G.4^-14 * G.1 * G.2 * G.4^-14 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^31 * G.1 * G.3 * G.4^-12 * G.2 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-22 * G.1 * G.4^-5 * G.1 * G.4^-17 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^28 * G.2 * G.4 * G.2 * G.4^15 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-35 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4 * G.2 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^26 * G.3 * G.1 * G.4 * G.3 * G.4^-5 * G.1 * G.4^10 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^17 * G.2 * G.4^-13 * G.1 * G.2 * G.1 * G.4^12 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-11 * G.1 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.2 * G.4^9 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-2 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.1^2 * G.4^-2 * G.1 * G.3 * G.4^-5 * G.1 * G.3 * G.4^-1 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-3 * G.1 * G.4^5 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^11 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^4 * G.3 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^9 * G.2 * G.4^2 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-6 * G.1 * G.4^4 * G.2 * G.1 * G.4^10 * G.2 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^9 * G.1 * G.4^2 * G.3 * G.4^-4 * G.2 * G.4^6 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-8 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^10 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^9 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1^2 * G.4^-3 * G.1 * G.4^3 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.4^-7 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.4^-12 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-11 * G.1 * G.4^-5 * G.1 * G.4^-6 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-11 * G.1 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.1^2 * G.4^-2 * G.1 * G.3 * G.4^-5 * G.1 * G.3 * G.1 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^10 * G.1 * G.4^-1 * G.1 * G.4^11 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-4 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^11 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^4 * G.2 * G.4^-1 * G.3 * G.4^-5 * G.1 * G.4^11 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^9 * G.1 * G.4 * G.1 * G.4^12 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^6 * G.3 * G.4^-2 * G.2 * G.1^2 * G.4^2 * G.3 * G.4^-9 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-8 * G.1 * G.4^2 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.4^-9 * G.1 * G.4^2 * G.2 * G.1 * G.4^6 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-11 * G.1 * G.4 * G.2 * G.4^5 * G.3 * G.4^-4 ] Genus 87 action of group of order 352 via quadrangle group [ 2, 2, 2, 88 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.4^5 ] Genus 87 action of group of order 348 via quadrangle group [ 2, 2, 2, 174 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-43 * G.2 * G.3 * G.4^-43 ] Genus 87 action of group of order 348 via quadrangle group [ 2, 2, 2, 174 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-80 * G.2 * G.4^-7 ] Genus 87 action of group of order 348 via quadrangle group [ 2, 2, 2, 174 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^73 * G.2 * G.1 * G.4^13 ] Largest orientation-preserving group for genus 87 has order 2064 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 87 has order 2064 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 87 has order 1440 ... group action with signature (0; +; [-]; {(2,4,90)}) Largest chiral group for genus 87 has order 2064 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 88 has order 720 ... group action with signature (0; +; [-]; {(2,4,90)}) Check total 395 : 304 chiral, 91 reflexible, with 35 non-orientable quotient actions Genus 88 actions: Genus 88 action of group of order 712 via triangle group [ 2, 4, 178 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-178 ] Genus 88 action of group of order 704 via triangle group [ 2, 4, 352 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-40 * G.1 * G.2^-1 * G.3^-135 ] Genus 88 action of group of order 576 via triangle group [ 2, 6, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-17 * G.1 * G.3^8 * G.2 * G.3^-6 ] Genus 88 action of group of order 540 via triangle group [ 2, 6, 90 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-50 * G.1 * G.3 * G.2 * G.1 * G.3^20 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 88 action of group of order 540 via triangle group [ 2, 6, 90 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-6 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^6 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-10 ] Genus 88 action of group of order 540 via triangle group [ 2, 6, 90 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-3 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-10 ] Genus 88 action of group of order 540 via triangle group [ 2, 6, 90 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^68 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-5 * G.1 * G.3^14 ] Genus 88 action of group of order 528 via triangle group [ 2, 6, 264 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-50 * G.1 * G.3^20 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 88 action of group of order 460 via triangle group [ 2, 10, 46 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-12 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-16 ] Genus 88 action of group of order 440 via triangle group [ 2, 10, 220 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-11 * G.1 * G.3^19 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 88 action of group of order 432 via triangle group [ 2, 12, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^8 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 88 action of group of order 432 via triangle group [ 2, 12, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^-5 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 88 action of group of order 432 via triangle group [ 2, 12, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^12, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1 ] Genus 88 action of group of order 432 via triangle group [ 2, 12, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^2 * G.2 * G.1 * G.3^15 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^3 ] Genus 88 action of group of order 416 via triangle group [ 2, 16, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-10 * G.3^-1 * G.2, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.2^-1 * G.3^-6 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^2 * G.1 * G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^4, G.3^-4 * G.1 * G.3^3 * G.2 * G.1 * G.3^7 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-1 * G.2^4)^2, G.2^-5 * G.3 * G.2^5 * G.1 * G.2^-6 * G.3^-1 * G.1 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-3 * G.3^2 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3 * G.2^4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2^4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 88 action of group of order 432 via triangle group [ 2, 18, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2, G.2 * G.1 * G.3 * G.2^4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 88 action of group of order 396 via triangle group [ 2, 18, 198 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 88 action of group of order 374 via triangle group [ 2, 34, 187 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^4 * G.2^-4 * G.3^4 ] Genus 88 action of group of order 378 via triangle group [ 2, 42, 63 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-8 * G.3^4 * G.2^-4 * G.3^5 ] Genus 88 action of group of order 378 via triangle group [ 2, 42, 63 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 88 action of group of order 378 via triangle group [ 2, 42, 63 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-2 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-7 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 88 action of group of order 368 via triangle group [ 2, 46, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-10 * G.2^12 * G.3^-4 * G.2^18 * G.3^-2 ] Genus 88 action of group of order 360 via triangle group [ 2, 90, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-56 * G.2^34 ] Genus 88 action of group of order 354 via triangle group [ 2, 177, 354 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^121 * G.2^-54 * G.3 ] Genus 88 action of group of order 356 via triangle group [ 2, 178, 178 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^56 * G.3^-122 ] Genus 88 action of group of order 352 via triangle group [ 2, 352, 352 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^55 * G.3^-121 ] Genus 88 action of group of order 360 via triangle group [ 3, 10, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 88 action of group of order 356 via triangle group [ 4, 4, 89 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^2 * G.3^5 ] Genus 88 action of group of order 356 via triangle group [ 4, 4, 89 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-1 ] Genus 88 action of group of order 356 via triangle group [ 4, 4, 89 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^75 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 88 action of group of order 352 via triangle group [ 4, 4, 176 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^75 * G.2 * G.1^-1 * G.3^12 ] Genus 88 action of group of order 360 via triangle group [ 4, 6, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.3^-1 * G.2)^2, G.3^10 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 88 action of group of order 696 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 88 action of group of order 356 via quadrangle group [ 2, 2, 2, 89 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-44 * G.2 * G.1 * G.3 * G.4^-44 ] Genus 88 action of group of order 356 via quadrangle group [ 2, 2, 2, 89 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-82 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 88 action of group of order 356 via quadrangle group [ 2, 2, 2, 89 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-89 ] Genus 88 action of group of order 352 via quadrangle group [ 2, 2, 2, 176 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-44 * G.1 * G.4^-44 ] Genus 88 action of group of order 352 via quadrangle group [ 2, 2, 2, 176 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-81 * G.1 * G.3 * G.4^-6 ] Genus 88 action of group of order 352 via quadrangle group [ 2, 2, 2, 176 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-73 * G.1 * G.2 * G.4^-14 ] Largest orientation-preserving group for genus 88 has order 712 ... group action with signature (0: +; [2,4,178]; {-}) Largest group with or without reflections for genus 88 has order 1424 ... group action with signature (0; +; [-]; {(2,4,178)}) Largest group with reflections for genus 88 has order 1424 ... group action with signature (0; +; [-]; {(2,4,178)}) Largest chiral group for genus 88 has order 696 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 89 has order 696 ... group action with signature (0; +; [2]; {(2,4)}) Check total 164 : 122 chiral, 42 reflexible, with 10 non-orientable quotient actions Genus 89 actions: Genus 89 action of group of order 2640 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 2640 via triangle group [ 2, 3, 10 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^10, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 89 action of group of order 960 via triangle group [ 2, 4, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1, G.3^-15 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2, G.3^-8 * G.1 * G.3^4 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-32 * G.1 * G.3^8 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-5 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-4 * G.2 * G.3^6 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-29 * G.1 * G.3^11 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2, G.3 * G.2 * G.3^-5 * G.1 * G.3^6 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^4 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-5 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3^-3 * G.1 * G.3^8 * G.2 * G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^4 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 768 via triangle group [ 2, 4, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, (G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3)^2 ] Genus 89 action of group of order 736 via triangle group [ 2, 4, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-74 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.3^-8 ] Genus 89 action of group of order 720 via triangle group [ 2, 4, 180 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-180 ] Genus 89 action of group of order 712 via triangle group [ 2, 4, 356 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2^-1 * G.3^-136 ] Genus 89 action of group of order 1320 via triangle group [ 2, 5, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 89 action of group of order 1320 via triangle group [ 2, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 89 action of group of order 672 via triangle group [ 2, 6, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 672 via triangle group [ 2, 6, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^4 * G.2^2 * G.3^-2 * G.2 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 89 action of group of order 672 via triangle group [ 2, 6, 14 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 89 action of group of order 552 via triangle group [ 2, 6, 69 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-10 ] Genus 89 action of group of order 534 via triangle group [ 2, 6, 267 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-51 * G.1 * G.3^20 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-4)^2, G.3^10, G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^3 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^2 * G.2^3 * G.1 * G.3^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-4)^2, G.3^10 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^10, G.3^-3 * G.1 * G.2^-2 * G.3^-4 * G.2 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.2 * G.3^-4)^2, G.3^10 ] Genus 89 action of group of order 640 via triangle group [ 2, 8, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^10, G.3^-3 * G.1 * G.2^-2 * G.3^-4 * G.2 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-8 * G.1 * G.3^11 * G.2^-1 * G.3^-12 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^7 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-6 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.3^-6 * G.1 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.3^-10 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-5 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 89 action of group of order 512 via triangle group [ 2, 8, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-5 ] Genus 89 action of group of order 480 via triangle group [ 2, 8, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-24 * G.1 * G.3^21 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-12 ] Genus 89 action of group of order 480 via triangle group [ 2, 8, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-46 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-11 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-4)^2 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^12 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.3^9 * G.2 * G.1 * G.2 * G.3^-5 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4, G.3^-2 * G.1 * G.2^-3 * G.3^-3 * G.2^2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 89 action of group of order 480 via triangle group [ 2, 12, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-3 * G.2)^2 ] Genus 89 action of group of order 448 via triangle group [ 2, 14, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-3 * G.2^2, G.2^14 ] Genus 89 action of group of order 448 via triangle group [ 2, 14, 28 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-1 * G.2^2 * G.3^-2, G.2^14 ] Genus 89 action of group of order 480 via triangle group [ 2, 15, 15 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-7 * G.3 * G.2^-1 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-3 * G.3^3 * G.2^-9 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^-2 * G.3 * G.2^-4 * G.3^2 * G.2^-9 * G.3 * G.2^-1 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2^-4 * G.3^4 * G.2^-1 * G.3 * G.2^-6 * G.3 * G.2^-3 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-4, G.2^-1 * G.3^8 * G.2^-7 * G.3 * G.2^-2 * G.3 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2^-1 * G.3^4 * G.2^-1 * G.3 * G.2^-10 * G.3^2 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.2^-1 * G.3^4 * G.2^-2 * G.3 * G.2^-6 * G.3^4 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-5 * G.3^2 * G.2^-9 * G.3^4 ] Genus 89 action of group of order 440 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^-4 * G.3 * G.2^-3 * G.3 * G.2^-7 * G.3^2 * G.2^-2 ] Genus 89 action of group of order 384 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2^-4 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^2 * G.3^-2 * G.2^9 * G.3^-2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-19 * G.3^4 * G.2^-5 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 2, 32, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.2^2 * G.3^-2 * G.2^9 * G.3^-2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^-1 * G.3^3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-6 * G.3^3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-48 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-6 * G.3^3 * G.2^-12 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-10 * G.3^4 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-11 * G.2^12 * G.3^-4 * G.2^20 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-32 * G.3^3 * G.2^-12 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^2 * G.3^-13 * G.2^11 * G.3^-4 * G.2 * G.3^-15 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-12 * G.3 * G.2^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^3 * G.3^-4 * G.2^3 * G.3^-1 * G.2^6 * G.3^-3 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-9 * G.3^2 * G.2^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-9 * G.3^2 * G.2^-2 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-9 * G.3^2 * G.2^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^-1 * G.2^6 * G.3^-3 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^-1 * G.2^6 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.3^-2 * G.2^2 * G.3^-1 * G.2^2 * G.3^-5 ] Genus 89 action of group of order 384 via triangle group [ 2, 48, 48 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^4)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 89 action of group of order 368 via triangle group [ 2, 92, 92 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-57 * G.2^33 * G.3^-1 ] Genus 89 action of group of order 358 via triangle group [ 2, 179, 358 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^122 * G.2^-56 ] Genus 89 action of group of order 360 via triangle group [ 2, 180, 180 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^57 * G.3^-122 * G.2 ] Genus 89 action of group of order 356 via triangle group [ 2, 356, 356 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^56 * G.3^-121 * G.2 ] Genus 89 action of group of order 1320 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 1320 via triangle group [ 3, 3, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 89 action of group of order 672 via triangle group [ 3, 3, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1^-1 * G.3 * G.2^-1 * G.3^-1)^2, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 89 action of group of order 672 via triangle group [ 3, 3, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1^-1 * G.3 * G.2^-1 * G.3^-1)^2, (G.2 * G.1^-1 * G.3)^3 ] Genus 89 action of group of order 672 via triangle group [ 3, 3, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3^2 * G.2)^2, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-2 * G.1 ] Genus 89 action of group of order 672 via triangle group [ 3, 3, 14 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3^2 * G.2)^2, (G.2 * G.1^-1 * G.3)^3 ] Genus 89 action of group of order 480 via triangle group [ 3, 4, 20 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.3^4 * G.2^-1 * G.3^-5, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 660 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^2, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 89 action of group of order 660 via triangle group [ 3, 5, 5 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 89 action of group of order 660 via triangle group [ 3, 5, 5 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 89 action of group of order 660 via triangle group [ 3, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.3^-1 * G.2)^3, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^8 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3, G.3 * G.2^-3 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.2^8, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^9 * G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^15 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-5 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-3 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-3 * G.1^-1 * G.3^3 * G.2 * G.3^-5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^4 * G.2^-1 * G.3^-6 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^-3 * G.2 * G.1^-1 * G.3^2 * G.2^2, G.3^5 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-15 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-3 * G.1^-1 * G.3^2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.2 * G.3^-2 * G.1^-2 * G.3^3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-5 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^-16 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^5 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^15 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-3 * G.1 * G.3^2 * G.2 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^2 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.1^-2 * G.3^3 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^9 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3 * G.2 * G.3^-5 * G.1 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-7 * G.1^-1 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-10 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-5 * G.1^-1 * G.2 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^10 * G.2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^5 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^5 * G.2 * G.3^-1 * G.1 * G.3^5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.3^-4 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-13 * G.1^-1 * G.3^3 * G.2 * G.3^-3 * G.1^-1 * G.3^3 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^14 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3^-6 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^-2 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3^4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3, G.1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^10 * G.2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^3 * G.2 * G.1^-1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^2, G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^-2 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^5 * G.2 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^9 * G.2 * G.3^-5 * G.1^-1 * G.3^9 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^13 * G.2^-1 * G.3^-5 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-12 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.3^19 * G.2 * G.3^-3 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-10 * G.1^-1 * G.3 * G.2^-1 * G.3^-6 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.3^3 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^3 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^5 * G.2 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^6 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-4 ] Genus 89 action of group of order 384 via triangle group [ 4, 4, 24 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.3^3 * G.2 * G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 89 action of group of order 368 via triangle group [ 4, 4, 46 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-8 * G.1 ] Genus 89 action of group of order 360 via triangle group [ 4, 4, 90 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^6 * G.2 * G.3^-4 * G.1 * G.3 * G.2 * G.3^-4 * G.1^-1 * G.2 * G.1^-1 ] Genus 89 action of group of order 360 via triangle group [ 4, 4, 90 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^11 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^4 ] Genus 89 action of group of order 360 via triangle group [ 4, 4, 90 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^76 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 89 action of group of order 356 via triangle group [ 4, 4, 178 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^75 * G.2^-1 * G.1 * G.3^13 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, (G.3^-1 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.2^-2 * G.3^-1 * G.1^2 * G.3^2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-2 * G.3^-1 * G.1^2 * G.3^2 * G.1^-1, G.1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3, G.1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.2^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, (G.1 * G.2^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, (G.1 * G.3^2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, (G.1 * G.3^2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.3^-2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.2^-2 * G.3^-1 * G.1^2 * G.3^2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2^-2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, (G.1 * G.2^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1, (G.1 * G.2^-1)^4, (G.1 * G.3^-1 * G.2^2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, (G.2 * G.3^-1)^4, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.3^-2 * G.2 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1)^4, G.3^8, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, (G.2 * G.3^-1)^4, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.3^-1 * G.1^-1 * G.3^2, G.2^6, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, (G.1 * G.3^-2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, (G.1 * G.3^-2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3^-2)^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, (G.1 * G.2^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3^-2)^2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2 * G.3^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.2^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.1, (G.2 * G.3^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.2^2 * G.1^2 * G.2^-1 * G.3 * G.2, (G.1 * G.3^2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-1)^4 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.2 * G.1^-2 * G.3^3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2^2, (G.1 * G.3^-2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.2^-1)^4, (G.1 * G.3^-1 * G.2^2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.1 * G.3^-1 * G.2^2)^2, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^8, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^8, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.1 * G.3^-1 * G.2^2)^2, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.1 * G.3^-2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.1 * G.3^-1 * G.1^-1 * G.3^3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2, G.1^-1 * G.2^2 * G.1^-2 * G.3 * G.2 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1^-1 * G.2^2 * G.1^-2 * G.3 * G.2 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.1 * G.3^-1 * G.2^2)^2, (G.1^-1 * G.3 * G.2^2)^2, G.1 * G.3^-2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, (G.1 * G.3^2 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, (G.2 * G.3^-1 * G.2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^8, G.3^-2 * G.2^2 * G.1^-1 * G.3 * G.2^3, G.3^-3 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.2 * G.3^-1)^4, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3 * G.2^-1)^2, G.2^6, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^8, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-2 * G.3, G.3^-3 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.3^-3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.3^2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2, G.3 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1 * G.3^2, G.2^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2, G.3 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.2^-2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^8 ] Genus 89 action of group of order 384 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^44 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^22 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^22 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^22 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^44 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^22 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 704 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^22 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^22 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.3 * G.2 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-2 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.3 * G.1 * G.3 * G.1 * G.4)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 528 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.3 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 440 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^18, G.1 * G.4^-3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^2 * G.3 * G.4^-8 * G.1 * G.4 * G.2 * G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-5 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-7 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, G.3 * G.4^3 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 89 action of group of order 396 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^15 * G.1^2 * G.4^9 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-11 * G.2 * G.4^4 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^5 * G.3 * G.4^-11 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^10 * G.3 * G.4^-5 * G.2 * G.4^-2 * G.1 * G.2 * G.4 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^8 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^11 * G.2 * G.4^-1 * G.3 * G.4^-5 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-10 * G.1 * G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-7 * G.1 * G.4^7 * G.3 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^19 * G.3 * G.1^2 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-3 * G.2 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^6 * G.2 * G.4 * G.1^2 * G.4^3 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-5 * G.2 * G.1 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^3 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-4 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^3 * G.2 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-10 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.3 * G.4^-6 * G.1^2 * G.4^-1 * G.1 * G.4^-10 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-4 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-8 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.4^9 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^8 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^7 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^9 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-12 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^10 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-7 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^10 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^4 * G.3 * G.4^-3 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^8 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4^15 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^7 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^5 * G.3 * G.4^-1 * G.1^2 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-11 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8 * G.3 * G.2 * G.1 * G.4^15 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^9 * G.2 * G.4^-2 * G.3 * G.4^-7 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.3 * G.4^-13 * G.1 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^4 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1, G.4^-1 * G.2 * G.4^4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^5 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^7 * G.1 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.1 * G.4^5 * G.1 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1, G.4^-1 * G.2 * G.4^4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^5 * G.2 * G.4^-1 * G.1^2 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^5 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-5 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.1 * G.4^5 * G.1 * G.4^-3 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.1 * G.4^5 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^5 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-3 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^5 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^6, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-5 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.2 * G.1 * G.4^5 * G.1^2 * G.2 * G.4^-4 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-5 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^-1 * G.3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^6 * G.2 * G.4 * G.1^2 * G.2 * G.4^2 * G.2 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4^6 * G.1 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^4 * G.2 * G.4^-3 * G.1 * G.4^4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^3 * G.2 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.4 * G.3 * G.2 * G.4^3 * G.1 * G.4 * G.3 * G.1 * G.4^-5 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-2 * G.2, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^2 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^5, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^8 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^3 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^5 * G.1 * G.4 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^5 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^6, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-5 * G.2 * G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-5 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^13 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^13 * G.3 * G.4^-1 * G.1 * G.2 * G.4^9 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-3 * G.2 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-2 * G.1^2 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^6 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-6 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4^-2 * G.1 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-2 * G.1^2 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-6 * G.2 * G.4^2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.1 * G.4^-5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-5 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^15 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^12 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^6 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^6 * G.1 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.1 * G.3 * G.2 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4^4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^5 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1^2 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.4^2 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-16 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^9 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^24 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-10 * G.1 * G.4^7 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^12 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^17 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.4^5 * G.2 * G.4^-3 * G.1 * G.4 * G.1^2 * G.2 * G.4^-10 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-6 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-3 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.1 * G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-4 * G.2 * G.4 * G.3 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^3 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-2 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4^4 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.1 * G.4^4 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^2 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^2 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^5 * G.2 * G.4 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4^5 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-3 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-6 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-5 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^2 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-2 * G.1 * G.4^4 * G.3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-3 * G.2 * G.4^5 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.1^2 * G.4^3 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-2 * G.2 * G.4^3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^4 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4^7 * G.3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.4^-3 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^6 * G.3 * G.1 * G.4^2 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-5 * G.1 * G.4^4 * G.3 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4 * G.2 * G.4^-4 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^3 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^6 * G.2 * G.4^-1 * G.1 * G.4^4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.2)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4^-1)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.2)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, (G.1 * G.2)^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6, G.4^3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.2)^6 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-3)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 89 action of group of order 384 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^12 * G.3 * G.4^-1 * G.2 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-6 * G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^6 * G.3 * G.1^2 * G.2 * G.4^16 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-3 * G.2 * G.4^4 * G.1 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-17 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^17 * G.3 * G.1 * G.4^5 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^14 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1^2 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-16 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-18 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^17 * G.2 * G.1 * G.4^5 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^6 * G.2 * G.4^-5 * G.1 * G.3 * G.2 * G.1 * G.4^10 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^4 * G.2 * G.4^-6 * G.1 * G.4 * G.1 * G.4^-5 * G.1 * G.4^6 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-46 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-21 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-13 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^46 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^24 * G.3 * G.4^-5 * G.1 * G.2 * G.4^16 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^21 * G.2 * G.4^-5 * G.1 * G.4^5 * G.2 * G.1 * G.4^13 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^19 * G.2 * G.4^-7 * G.1 * G.2 * G.4^-1 * G.1 * G.4^17 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-15 * G.2 * G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^19 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^46 ] Genus 89 action of group of order 368 via quadrangle group [ 2, 2, 2, 46 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-17 * G.1 * G.4^20 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-16 * G.2 * G.4 * G.3 * G.4^-17 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^7 * G.3 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-17 * G.2 * G.4 * G.3 * G.4^-14 * G.2 * G.4 * G.1 * G.4^9 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-39 * G.1 * G.3 * G.4^-5 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^37 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.2 * G.4^-17 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-20 * G.1 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-22 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-14 * G.1 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.1, G.4^-10 * G.1 * G.4^-4 * G.1 * G.4^-4 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-2 * G.2 * G.4 * G.3 * G.4^-3 * G.1 * G.4^-11 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1 * G.3 * G.4^-4 * G.2, G.4^-1 * G.1 * G.4^8 * G.3 * G.1 * G.3 * G.4^-7 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^7 * G.2 * G.1 * G.4^3 * G.1^2 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^12 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^3 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^7 * G.2 * G.1 * G.4^3 * G.2 * G.1 * G.4^6 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-90 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7 * G.1^2 * G.4^-83 ] Genus 89 action of group of order 360 via quadrangle group [ 2, 2, 2, 90 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^61 * G.2 * G.4^-8 * G.1 * G.2 * G.1 * G.4^19 ] Genus 89 action of group of order 356 via quadrangle group [ 2, 2, 2, 178 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-44 * G.2 * G.3 * G.4^-44 ] Genus 89 action of group of order 356 via quadrangle group [ 2, 2, 2, 178 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-82 * G.2 * G.4^-7 ] Genus 89 action of group of order 356 via quadrangle group [ 2, 2, 2, 178 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-74 * G.1 * G.2 * G.4^-14 ] Largest orientation-preserving group for genus 89 has order 2640 ... group action with signature (0: +; [2,3,10]; {-}) Largest group with or without reflections for genus 89 has order 5280 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest group with reflections for genus 89 has order 5280 ... group action with signature (0; +; [-]; {(2,3,10)}) Largest chiral group for genus 89 has order 768 ... group action with signature (0: +; [2,4,48]; {-}) Largest non-orientable group for non-orientable genus 90 has order 1320 ... group action with signature (0; +; [-]; {(2,5,6)}) Check total 2048 : 1142 chiral, 906 reflexible, with 162 non-orientable quotient actions Genus 90 actions: Genus 90 action of group of order 744 via triangle group [ 2, 4, 93 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-74 * G.1 * G.3^11 * G.2^-1 * G.3^-7 ] Genus 90 action of group of order 728 via triangle group [ 2, 4, 182 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-182 ] Genus 90 action of group of order 720 via triangle group [ 2, 4, 360 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-42 * G.1 * G.2^-1 * G.3^-137 ] Genus 90 action of group of order 552 via triangle group [ 2, 6, 92 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^55 * G.2 * G.1 * G.3^20 * G.2 * G.1 * G.3 * G.2 * G.3^-7 * G.1 * G.3^6 ] Genus 90 action of group of order 712 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 90 action of group of order 712 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3 ] Genus 90 action of group of order 712 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 90 action of group of order 712 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-3 ] Genus 90 action of group of order 496 via triangle group [ 2, 8, 62 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-38 * G.1 * G.3^3 * G.2 * G.1 * G.3^8 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 ] Genus 90 action of group of order 456 via triangle group [ 2, 12, 38 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-4 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-16 ] Genus 90 action of group of order 448 via triangle group [ 2, 14, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^7 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 90 action of group of order 420 via triangle group [ 2, 14, 210 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, (G.2^-2 * G.3^4 * G.2^-1)^2, G.3^2 * G.2 * G.3^-8 * G.1 * G.3^4 * G.2^-1 * G.3^-13 * G.1 * G.3 ] Genus 90 action of group of order 440 via triangle group [ 2, 20, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^3 * G.1 * G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^5, G.3^-15 * G.1 * G.2 * G.3^-6 ] Genus 90 action of group of order 420 via triangle group [ 2, 21, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 90 action of group of order 396 via triangle group [ 2, 22, 198 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-9 * G.3^4 * G.2^-5 * G.3^4 ] Genus 90 action of group of order 390 via triangle group [ 2, 26, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^13 * G.2^-1 * G.3^-1 * G.1 ] Genus 90 action of group of order 380 via triangle group [ 2, 38, 190 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^-3 * G.2^9 * G.3^-4 * G.2^21 * G.3^-1 ] Genus 90 action of group of order 372 via triangle group [ 2, 62, 186 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-26 * G.2^13 * G.3^-2 * G.2^20 ] Genus 90 action of group of order 370 via triangle group [ 2, 74, 185 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.2 * G.3^-1 * G.2^10 * G.3^-4 * G.2^21 ] Genus 90 action of group of order 368 via triangle group [ 2, 92, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-9 * G.2^12 * G.3^-4 * G.2^19 * G.3^-1 ] Genus 90 action of group of order 372 via triangle group [ 2, 93, 93 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-89 * G.3 * G.2^-1 ] Genus 90 action of group of order 366 via triangle group [ 2, 122, 183 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-25 * G.2^13 * G.3^-2 * G.2^18 * G.3^-2 ] Genus 90 action of group of order 362 via triangle group [ 2, 181, 362 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^123 * G.2^-56 * G.3 ] Genus 90 action of group of order 364 via triangle group [ 2, 182, 182 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^58 * G.3^-124 ] Genus 90 action of group of order 360 via triangle group [ 2, 360, 360 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^57 * G.3^-123 ] Genus 90 action of group of order 543 via triangle group [ 3, 3, 181 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-9 ] Genus 90 action of group of order 543 via triangle group [ 3, 3, 181 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 90 action of group of order 364 via triangle group [ 4, 4, 91 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^77 * G.2^-1 * G.1^-1 * G.3^13 ] Genus 90 action of group of order 364 via triangle group [ 4, 4, 91 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 90 action of group of order 364 via triangle group [ 4, 4, 91 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^-3, G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2 ] Genus 90 action of group of order 360 via triangle group [ 4, 4, 180 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^76 * G.2^-1 * G.1 * G.3^13 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-4 * G.2 * G.1^2 * G.4^5 * G.3 * G.4^-1 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.3 * G.1 * G.4^2 * G.2 * G.4^4 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^3 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-45 * G.2 * G.1 * G.3 * G.4^-45 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^83 * G.3 * G.1 * G.2 * G.4^7 ] Genus 90 action of group of order 364 via quadrangle group [ 2, 2, 2, 91 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^71 * G.1^2 * G.4^20 ] Genus 90 action of group of order 360 via quadrangle group [ 2, 2, 2, 180 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-45 * G.1 * G.4^-45 ] Genus 90 action of group of order 360 via quadrangle group [ 2, 2, 2, 180 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7 * G.1 * G.3 * G.4^-82 ] Genus 90 action of group of order 360 via quadrangle group [ 2, 2, 2, 180 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^61 * G.2 * G.4^-8 * G.1 * G.4^20 ] Largest orientation-preserving group for genus 90 has order 744 ... group action with signature (0: +; [2,4,93]; {-}) Largest group with or without reflections for genus 90 has order 1488 ... group action with signature (0; +; [-]; {(2,4,93)}) Largest group with reflections for genus 90 has order 1488 ... group action with signature (0; +; [-]; {(2,4,93)}) Largest chiral group for genus 90 has order 712 ... group action with signature (0: +; [2,8,8]; {-}) Largest non-orientable group for non-orientable genus 91 has order 744 ... group action with signature (0; +; [-]; {(2,4,93)}) Check total 43 : 4 chiral, 39 reflexible, with 8 non-orientable quotient actions Genus 91 actions: Genus 91 action of group of order 1512 via triangle group [ 2, 3, 21 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-6 * G.1 * G.3^2 * G.2^2 * G.1 * G.3^3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^2 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 91 action of group of order 1350 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^17 * G.2 * G.3^-5 * G.1 * G.3^2 * G.2^-1 * G.3^-6 * G.1 * G.3^4 ] Genus 91 action of group of order 1296 via triangle group [ 2, 3, 36 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-8 * G.1 * G.3^2 * G.2^-1 * G.1 * G.3^5 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 1296 via triangle group [ 2, 3, 36 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^5 * G.2^-1 * G.3^-6, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 91 action of group of order 3600 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2, G.2 * G.3^-3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-2)^4 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2)^4, G.2^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-3 * G.1 * G.3, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-2)^4 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3^-2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^3 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, (G.3^-2 * G.2 * G.3^-1)^3 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5 ] Genus 91 action of group of order 1440 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 1200 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, G.3^10, (G.2 * G.3^-1)^6, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 1080 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 1080 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 1080 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 91 action of group of order 1080 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^3 * G.2^-1 * G.3 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-1)^6 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2 * G.3^-1)^6, G.1 * G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-4 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.2 * G.3^-1, G.3^-2 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2 * G.3^-1)^6, G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-8 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6 ] Genus 91 action of group of order 864 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-4 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.3^2 * G.2 * G.3^-6 * G.2 * G.1 * G.3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-9 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1, G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.3^2 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.3^-6 * G.2 * G.1 * G.3 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-12 * G.1 * G.3^2 * G.2 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 800 via triangle group [ 2, 4, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-11 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^12 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 792 via triangle group [ 2, 4, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, (G.2 * G.3^-1)^6, G.1 * G.3 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 760 via triangle group [ 2, 4, 76 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-17 * G.1 * G.3 * G.2 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 760 via triangle group [ 2, 4, 76 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-17 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^7 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 736 via triangle group [ 2, 4, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-74 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 91 action of group of order 736 via triangle group [ 2, 4, 184 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-184 ] Genus 91 action of group of order 728 via triangle group [ 2, 4, 364 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-43 * G.1 * G.2^-1 * G.3^-138 ] Genus 91 action of group of order 1800 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 91 action of group of order 864 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.3^2 * G.2^-1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 864 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^8, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 864 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 91 action of group of order 864 via triangle group [ 2, 6, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 91 action of group of order 720 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 2, 6, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 * G.2 ] Genus 91 action of group of order 648 via triangle group [ 2, 6, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-3 * G.1 * G.2^-2 * G.3^-5, G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 594 via triangle group [ 2, 6, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-11 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 558 via triangle group [ 2, 6, 93 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^76 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 91 action of group of order 546 via triangle group [ 2, 6, 273 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^74 * G.2 * G.1 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^4 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, G.3^8, G.2 * G.1 * G.3 * G.2^4 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2, (G.2^3 * G.3^-1)^3, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2^8, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-4 * G.3^-1 * G.1 * G.3^3, G.1 * G.3^2 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^8, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1 * G.2^-3 * G.3 * G.2^-1 * G.3^-3, G.2^-1 * G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, (G.2 * G.3^-1)^6 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.2^-3 * G.3^-5, G.1 * G.3^3 * G.2^-2 * G.3 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 576 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 91 action of group of order 600 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^10, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 540 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 91 action of group of order 540 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 ] Genus 91 action of group of order 540 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 540 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 91 action of group of order 480 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^12 ] Genus 91 action of group of order 480 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2^12 ] Genus 91 action of group of order 480 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^12 ] Genus 91 action of group of order 480 via triangle group [ 2, 12, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 91 action of group of order 450 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-9 * G.3 * G.1 * G.2^-5 ] Genus 91 action of group of order 448 via triangle group [ 2, 16, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^3 * G.1 * G.2^-1, G.3^-10 * G.1 * G.3^7 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 91 action of group of order 448 via triangle group [ 2, 16, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.3^-2 * G.1 * G.3^10 * G.2 * G.3^-2 * G.1 * G.2 * G.1 * G.3^9 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 416 via triangle group [ 2, 16, 208 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.1 * G.3^7 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-13 ] Genus 91 action of group of order 416 via triangle group [ 2, 16, 208 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-2 * G.1 * G.3^5 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-14 ] Genus 91 action of group of order 432 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-1 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^4 ] Genus 91 action of group of order 432 via triangle group [ 2, 18, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^-2 * G.3^2 * G.2^-3 * G.3^2 * G.2^-11 * G.3 * G.2^-2 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-2 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.2^4 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.3^3 * G.2^-3 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-6 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^8 * G.3^-1 * G.2^2 * G.3^-3 * G.2^5 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2^9 * G.3^-2 * G.2^2 * G.3^-2 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^5 * G.3^-3 * G.2^5 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-6 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^8 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-1 * G.2^6 * G.3^-5 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2 ] Genus 91 action of group of order 432 via triangle group [ 2, 24, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2^6 * G.3^-5 ] Genus 91 action of group of order 390 via triangle group [ 2, 30, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^8 * G.2^-2 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2^18 * G.3^-4 * G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2^13 * G.3^-3 * G.2 * G.3^-15 * G.2 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-2 * G.3^3 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-19 * G.2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^-1 * G.2^13 * G.3^-4 * G.2^19 * G.3^-3 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-3 * G.3^4 * G.2^-4 * G.3 * G.2^-2 * G.3 * G.2^-5 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-2 * G.3^3 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2^-6 * G.3^4 * G.2^-4 * G.3^4 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 91 action of group of order 400 via triangle group [ 2, 40, 40 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-13 * G.3 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 396 via triangle group [ 2, 44, 44 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.3^-5 * G.2 * G.3^-1 * G.2^4 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 392 via triangle group [ 2, 49, 49 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3^30 * G.2^-14 * G.3 * G.2^-1 ] Genus 91 action of group of order 392 via triangle group [ 2, 49, 49 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-2 * G.2, G.2^-3 * G.3^28 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-13 ] Genus 91 action of group of order 378 via triangle group [ 2, 54, 189 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-14 * G.3^4 * G.2^-6 * G.3^3 ] Genus 91 action of group of order 378 via triangle group [ 2, 63, 126 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^-28 * G.2^2 * G.3^-1 * G.2^10 * G.3^-4 * G.2 * G.3^-17 ] Genus 91 action of group of order 380 via triangle group [ 2, 76, 76 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-20 * G.2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 ] Genus 91 action of group of order 380 via triangle group [ 2, 76, 76 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2^16 * G.3^-4 * G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 366 via triangle group [ 2, 183, 366 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^124 * G.2^-58 ] Genus 91 action of group of order 368 via triangle group [ 2, 184, 184 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^59 * G.3^-124 * G.2 ] Genus 91 action of group of order 368 via triangle group [ 2, 184, 184 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-57 * G.2^32 * G.3^-1 * G.2 ] Genus 91 action of group of order 364 via triangle group [ 2, 364, 364 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^58 * G.3^-123 * G.2 ] Genus 91 action of group of order 675 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.2^-1 * G.3^-4 * G.1 * G.3^4 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1, G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 91 action of group of order 648 via triangle group [ 3, 3, 18 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^7 * G.2^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^3 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^4 * G.2 * G.1^-1 * G.2^-1 * G.3^-8 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1, G.2^-1 * G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1, G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 91 action of group of order 567 via triangle group [ 3, 3, 63 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 91 action of group of order 549 via triangle group [ 3, 3, 183 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^6 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 91 action of group of order 549 via triangle group [ 3, 3, 183 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 91 action of group of order 720 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^6, (G.2 * G.3^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 3, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 91 action of group of order 480 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.2 * G.3^-1)^2, G.1^-1 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 480 via triangle group [ 3, 4, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.3^-2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 91 action of group of order 504 via triangle group [ 3, 6, 7 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 91 action of group of order 450 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 450 via triangle group [ 3, 6, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^10 ] Genus 91 action of group of order 432 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^3 * G.1 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 3, 6, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 91 action of group of order 378 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2 ] Genus 91 action of group of order 378 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-2, G.3^-1 * G.1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 378 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-3 ] Genus 91 action of group of order 378 via triangle group [ 3, 6, 42 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^6 * G.2 ] Genus 91 action of group of order 366 via triangle group [ 3, 6, 122 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 ] Genus 91 action of group of order 366 via triangle group [ 3, 6, 122 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.1 * G.2^-2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^2, G.2^8, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1, (G.1^-1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^8, G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.1^-1 * G.3^-3 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-2)^2, G.2^8, (G.1 * G.3 * G.2^2)^2, G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.3 * G.2^2)^2 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^2, G.2^8, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^8, G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.1^-1 * G.3^-3 * G.2^2 ] Genus 91 action of group of order 432 via triangle group [ 3, 8, 8 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.2 * G.3^-2)^2, G.2^8, G.1^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-2 * G.3^-1, (G.1^-1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, (G.2 * G.3^-1)^4, (G.3^-1 * G.1^-1 * G.2)^3, (G.3 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, (G.2 * G.1^-1 * G.3)^3, (G.3^-1 * G.1^-1 * G.2)^3, G.2^-1 * G.3^-2 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.1^-1 * G.3)^3, (G.3 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^2 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1 * G.2, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.2)^3, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.2 * G.1 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, (G.2^-1 * G.1)^5 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.2^-1 * G.1)^3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.3^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.3^-1 * G.1)^3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, G.1 * G.3^-2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, (G.1 * G.2^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, (G.1 * G.2^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^-2 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, (G.1 * G.3^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.1^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.2^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1, (G.1 * G.2^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^2 * G.3^-1, G.1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, (G.1 * G.3^-1)^4 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.1^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2^-1 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 91 action of group of order 720 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.1^-1 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 91 action of group of order 600 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2)^2, (G.3 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 91 action of group of order 540 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 91 action of group of order 540 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2^2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 ] Genus 91 action of group of order 540 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2^2 * G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 91 action of group of order 540 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3, (G.1 * G.2^-1)^4, G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2, G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3^3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^-2 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3^2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2 * G.3^-5 * G.1 * G.3^5 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.3 * G.1^-1 * G.2^-1)^3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1, G.3^6 * G.2^-1 * G.1^-1 * G.3^5 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-1 * G.1^-1 * G.3^3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2, G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^4 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^-3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, G.3^12 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1, (G.1 * G.2^-1)^4 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^3, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3^3 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^-5 * G.1^-1 * G.3^4 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-5 * G.1^-1 * G.3^4 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^2 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.3^2 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2, G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1, (G.1 * G.2^-1)^4, G.1 * G.3 * G.2^-2 * G.1 * G.3^-3 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^-5 * G.1^-1 * G.3^4 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, G.3^4 * G.2 * G.1^-1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2, G.3^4 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^-8 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^8 * G.2 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.2 * G.1^-1 * G.3^8 * G.2 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^5 * G.2 * G.1 * G.3^4 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^10 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-4 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^4 * G.2^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 400 via triangle group [ 4, 4, 20 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^5 ] Genus 91 action of group of order 396 via triangle group [ 4, 4, 22 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1, G.3^5 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 ] Genus 91 action of group of order 380 via triangle group [ 4, 4, 38 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^3 * G.2 * G.3^-6 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-2 * G.1^-1 ] Genus 91 action of group of order 380 via triangle group [ 4, 4, 38 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^4 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2 * G.1^-1 * G.3^4 * G.2 * G.3^-2 * G.1^-1 ] Genus 91 action of group of order 368 via triangle group [ 4, 4, 92 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-8 * G.1^-1 ] Genus 91 action of group of order 368 via triangle group [ 4, 4, 92 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-8 * G.1 ] Genus 91 action of group of order 368 via triangle group [ 4, 4, 92 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-78 * G.1 * G.2 * G.3^-13 ] Genus 91 action of group of order 368 via triangle group [ 4, 4, 92 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^30 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-8 * G.1^-1 ] Genus 91 action of group of order 364 via triangle group [ 4, 4, 182 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^77 * G.2^-1 * G.1 * G.3^13 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.3^6, G.3 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.3^6, G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-2, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.2^-1 * G.1)^3, G.2^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.3 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3, G.2^-1 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1, (G.3^-1 * G.2)^3, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2^-2 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1, (G.3^-1 * G.1)^3, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^6, G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-2, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.3^-1 * G.1)^3, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1 * G.3^-1, G.3^6, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-2 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3, G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.3^-1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1 * G.3 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, (G.2 * G.1^-1 * G.3)^3 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.1^-1 * G.2^2 * G.1^2 * G.3 * G.1^-1 * G.3, (G.1^-1 * G.3 * G.2^2)^2, (G.1 * G.3^2 * G.2)^2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 91 action of group of order 432 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^6, G.2^2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^45 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, (G.3 * G.1)^9 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^5, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.1 * G.4)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^8, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^5, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, (G.2 * G.1)^5, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1 * G.4)^3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^5, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.4^-1 * G.2)^5, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.3 * G.1)^5, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.3 * G.1)^5, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.3 * G.1)^5, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1, (G.3 * G.1)^5, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.4^-1 * G.2)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^5 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^5, (G.1 * G.2)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^5, (G.1 * G.2)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, (G.4^-1 * G.2)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^5, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.1)^5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^6, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^15 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.3 * G.1)^15 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.3 * G.1)^15 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 720 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-5, (G.1 * G.3)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.4^-5, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-5, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^2 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^2 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^-2 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.2 * G.1)^5, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 600 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^45 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.3 * G.1)^9 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.3 * G.1)^15 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.3)^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^10 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, (G.3 * G.1)^15 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, (G.3 * G.1)^15 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 540 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^-3 * G.1 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-7, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-7, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-7, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-7, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^-7, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4^-1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2, G.4^-7, G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-7, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-7, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, (G.2 * G.1 * G.4)^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^-7, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, (G.2 * G.1 * G.4)^3, G.4^2 * G.2 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^-7, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.4^-7, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-7, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.4^2 * G.2 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-7, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-7, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-7, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-7, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-7, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-7, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-7, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-7, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-7, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.4^-7, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, (G.2 * G.1 * G.4)^3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^-7, (G.3 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-7, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-7, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-7, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7, G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-7, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^-7, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-7, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 91 action of group of order 504 via quadrangle group [ 2, 2, 2, 7 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-7, G.4^2 * G.2 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^3 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4^-2 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^6, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-2 * G.1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.3 * G.1)^5, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.2 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^8, (G.2 * G.1)^5, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.2 * G.1)^5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-2 * G.1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, (G.3 * G.1)^5, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, (G.2 * G.1)^5, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, (G.2 * G.1)^5, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, (G.3 * G.1)^15 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^10 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.3 * G.1)^15 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.4^-2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 480 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-3 * G.1 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.1 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-3 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^10 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^10 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^10 ] Genus 91 action of group of order 450 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^10 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.1^2 * G.4^6, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^12, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.1^2 * G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3, (G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-2 * G.1 * G.2 * G.4^5 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.4^5 * G.1 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.1 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^5 * G.1 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^5 * G.1 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^5 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-4 * G.1 * G.4^2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.1 * G.4^2 * G.1^2 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2, G.4 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.4^2 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^3 * G.2)^2, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.4^3 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^-1 * G.2 * G.4^-2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.3 * G.1)^9 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4^2 * G.2 * G.4^3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.1 * G.4 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-5 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^-5 * G.2 * G.1 * G.3 * G.4^-6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4^3 * G.2)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2^2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.4^5 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-5 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, (G.1 * G.3)^6, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-4 * G.2 * G.3 * G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^5 * G.1 * G.4^2 * G.3 * G.2 * G.4^4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.4^3 * G.2)^2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6, G.4 * G.2 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, (G.1 * G.3)^6, G.2 * G.4^4 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^12 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^12 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-5 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.3)^6 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, (G.1 * G.3)^6 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-6 * G.1 * G.4 * G.2 * G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^3 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, (G.1 * G.3)^6 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 420 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4^-3 * G.2 * G.4 * G.3 * G.1^2 * G.4^-3 * G.1 * G.4^-2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^20, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.1, G.4^-20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^8 * G.1 * G.4 * G.1^2 * G.4^6 * G.3 * G.4^-4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^9 * G.3 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.3 * G.4^-12 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1 * G.3 * G.4^-4 * G.2, G.4^-3 * G.1 * G.4^4 * G.2 * G.4^3 * G.3 * G.1 * G.4 * G.1 * G.4^-8 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4^20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^3 * G.3 * G.4^-4 * G.1 * G.4^10 * G.2 * G.4^2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2, G.4^20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^12 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^20 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^8 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^7 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.2 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.4^-7 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4 * G.2 * G.4^-9 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^6 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-8 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-6 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^12 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^13 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-4 * G.2 * G.3 * G.2 * G.4^4 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^-4 * G.1 * G.3 * G.1 * G.4^4 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5, G.2 * G.4 * G.3 * G.4^-3 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.4^-6 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.1 * G.4 * G.1 * G.4^5, G.2 * G.4 * G.3 * G.4^-3 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^5, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.4^3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^4 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 400 via quadrangle group [ 2, 2, 2, 20 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^5 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-5 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4 * G.3 * G.4^-1 * G.1 * G.4^5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, (G.1 * G.4 * G.2 * G.4 * G.2 * G.4)^2, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^6 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^3 * G.2 * G.4^6 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-6 * G.1 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^3 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-5 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-5 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 91 action of group of order 396 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-5 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-32 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-18 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^6 * G.3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^20 * G.3 * G.2 * G.4^5 * G.1^2 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4^12 * G.1 * G.4 * G.1^2 * G.4^6 * G.3 * G.4^-8 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^5 * G.3 * G.4^-9 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^14 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^32 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^32 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-11 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-12 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-20 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-23 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.4^-10 * G.1 * G.4 * G.2 * G.1 * G.4^13 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-15 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^6 * G.1^2 * G.3 * G.1 * G.4^-9 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^6 * G.1 * G.3 * G.4^-9 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^6 * G.1^2 * G.3 * G.1 * G.4^-9 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^6 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^-3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^4 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.4^-6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^5 * G.3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.1 * G.4^6 * G.3 * G.1 * G.4^7 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.4)^2, G.4^3 * G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^8 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-4 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1^2 * G.4^-6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.1 * G.4^6 * G.3 * G.1 * G.4^7 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^3 * G.2 * G.4^8 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-7 * G.1 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-4 * G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 * G.2 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 * G.3 * G.1^2 * G.4 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^7 * G.1 * G.4 * G.3 * G.4^-7 * G.2 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^-3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.3 * G.4^-9 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^6 * G.1 * G.3 * G.4^-9 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.3 * G.1^2 * G.4^-6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4^9 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-5 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-3 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^4 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.1^2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4 ] Genus 91 action of group of order 384 via quadrangle group [ 2, 2, 2, 32 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^9 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^11 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^3 * G.3 * G.4^-6 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4^2 * G.3 * G.4^-4 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^4 * G.3 * G.4^-2 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.1 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-8 * G.2 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1, G.4 * G.3 * G.4^-10 * G.2 * G.4^7 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-9 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.4^-5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2, G.4^11 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^9 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^13 * G.3 * G.1 * G.4^5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-11 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^5 * G.3 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-6 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-9 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.4^4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-3 * G.1 * G.4^10 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-8 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-7 * G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-5 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.2 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^10 ] Genus 91 action of group of order 380 via quadrangle group [ 2, 2, 2, 38 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^13 * G.2 * G.1 * G.4^5 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^20 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-3 * G.2 * G.4^13 * G.1^2 * G.4^6 * G.3 * G.4^-8 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.2 * G.4^2 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^17 * G.3 * G.4^-1 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-15 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-14 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^23 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^6 * G.3 * G.4^-7 * G.2 * G.1 * G.2 * G.4^17 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^24 * G.3 * G.1 * G.4^6 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-6 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-16 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-17 * G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1^2 * G.2 * G.4^-6 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^2 * G.2 * G.4^-7 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^12 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^5 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 91 action of group of order 372 via quadrangle group [ 2, 2, 2, 62 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-11 * G.1 * G.4^4 * G.2 * G.4^-15 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-92 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-84 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-70 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-16 * G.2 * G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^19 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-40 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-17 * G.1 * G.4^15 * G.2 * G.4^-4 * G.1 * G.4^2 * G.2 * G.4^-6 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-23 * G.1 * G.4^-1 * G.1 * G.4^-22 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-22 * G.2 * G.4^8 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-12 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^30 * G.1 * G.4^-9 * G.1 * G.4^7 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^22 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^24 * G.3 * G.4^-5 * G.1 * G.4 * G.2 * G.4^15 ] Genus 91 action of group of order 368 via quadrangle group [ 2, 2, 2, 92 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^19 * G.2 * G.4^-7 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^12 ] Genus 91 action of group of order 364 via quadrangle group [ 2, 2, 2, 182 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-45 * G.2 * G.3 * G.4^-45 ] Genus 91 action of group of order 364 via quadrangle group [ 2, 2, 2, 182 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^83 * G.3 * G.1 * G.4^7 ] Genus 91 action of group of order 364 via quadrangle group [ 2, 2, 2, 182 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^71 * G.1^2 * G.2 * G.1 * G.4^19 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.1, G.3^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1, (G.1 * G.3^-1)^6 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.3 * G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.4^-1 * G.3)^3, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1, (G.4^-1 * G.3)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.3)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, (G.4^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, (G.2 * G.4 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3 * G.2 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1 * G.4^-1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.3^-1, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3^-1)^2, (G.4^-1 * G.3)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.4^-1 * G.3)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, G.4 * G.2 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.2 * G.1)^3, G.4^-2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3^-1)^2, G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.1)^3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.2^-1 * G.3 * G.2^-1 * G.3 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1, (G.2^-1 * G.3 * G.2^-1 * G.3 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2^-1 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.4 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2^-2 * G.3 * G.2 * G.3 * G.1 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2 * G.4^-1)^2, G.4^4, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.2^-1 * G.3 * G.2^-1 * G.3 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.3 * G.1)^2, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1, (G.2^-1 * G.4^-1 * G.2 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1, (G.2^-1 * G.3 * G.1 * G.2^-1 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.2 * G.3 * G.2^-1 * G.4^2 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1)^3, G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.4^-1 * G.2^-1)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-1 * G.2^-1 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.4^-1 * G.2^-1)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^2 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, (G.3 * G.1)^3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.1 * G.2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.3 * G.1)^3, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 91 action of group of order 432 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Largest orientation-preserving group for genus 91 has order 3600 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 91 has order 7200 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 91 has order 7200 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 91 has order 1440 ... group action with signature (0: +; [2,4,8]; {-}) Largest non-orientable group for non-orientable genus 92 has order 1440 ... group action with signature (0; +; [-]; {(2,4,8)}) Check total 3317 : 2432 chiral, 885 reflexible, with 258 non-orientable quotient actions Genus 92 actions: Genus 92 action of group of order 2184 via triangle group [ 2, 3, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^-1 * G.3^-3 * G.1 * G.3^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 ] Genus 92 action of group of order 2184 via triangle group [ 2, 3, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 2184 via triangle group [ 2, 4, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, (G.2^-1 * G.3 * G.2^-1 * G.3^2)^3, G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 92 action of group of order 744 via triangle group [ 2, 4, 186 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-186 ] Genus 92 action of group of order 736 via triangle group [ 2, 4, 368 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-44 * G.1 * G.2^-1 * G.3^-139 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^3 * G.3^-1 ] Genus 92 action of group of order 1092 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.1 ] Genus 92 action of group of order 672 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^4 * G.2^2 * G.1 * G.3^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 672 via triangle group [ 2, 6, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^4 * G.2^2 * G.1 * G.3^3, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 92 action of group of order 624 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-3, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 92 action of group of order 624 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^-2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-3, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 624 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 92 action of group of order 624 via triangle group [ 2, 6, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 92 action of group of order 588 via triangle group [ 2, 6, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 92 action of group of order 588 via triangle group [ 2, 6, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 588 via triangle group [ 2, 6, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1, G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 92 action of group of order 588 via triangle group [ 2, 6, 42 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-6 ] Genus 92 action of group of order 564 via triangle group [ 2, 6, 94 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-57 * G.1 * G.3^15 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-19 ] Genus 92 action of group of order 552 via triangle group [ 2, 6, 276 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^74 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 92 action of group of order 528 via triangle group [ 2, 8, 33 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-23 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 92 action of group of order 496 via triangle group [ 2, 8, 124 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-38 * G.1 * G.3^3 * G.2 * G.1 * G.3^8 * G.2^-1 * G.3^-11 ] Genus 92 action of group of order 480 via triangle group [ 2, 10, 48 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^-34 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-5 ] Genus 92 action of group of order 460 via triangle group [ 2, 10, 230 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^30 * G.2 * G.3^-9 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 92 action of group of order 468 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-3 * G.3^3 * G.2^-1 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3^3 ] Genus 92 action of group of order 468 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2, G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^3 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 468 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-2 * G.3^3 ] Genus 92 action of group of order 468 via triangle group [ 2, 18, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-2 * G.3^3 ] Genus 92 action of group of order 414 via triangle group [ 2, 18, 207 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.1 * G.3^11 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 92 action of group of order 420 via triangle group [ 2, 30, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-2 * G.3^5 * G.2^-2 * G.3 * G.2^-5 * G.3 * G.2^-1 * G.3 * G.2^-8 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 420 via triangle group [ 2, 30, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3 * G.2^-6 * G.3^4 * G.2^-1 * G.3 * G.2^-11 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 420 via triangle group [ 2, 30, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-2 * G.3^2 * G.2^-9 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 420 via triangle group [ 2, 30, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3^6 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-9 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 376 via triangle group [ 2, 94, 188 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-59 * G.2^32 * G.3^-1 * G.2 ] Genus 92 action of group of order 370 via triangle group [ 2, 185, 370 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^125 * G.2^-58 * G.3 ] Genus 92 action of group of order 372 via triangle group [ 2, 186, 186 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^60 * G.3^-126 ] Genus 92 action of group of order 368 via triangle group [ 2, 368, 368 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^59 * G.3^-125 ] Genus 92 action of group of order 1092 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 92 action of group of order 1092 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-2 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 372 via triangle group [ 4, 4, 93 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-79 * G.1 * G.2 * G.3^-13 ] Genus 92 action of group of order 368 via triangle group [ 4, 4, 184 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-78 * G.1 * G.2^-1 * G.3^-13 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4^-1)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4^-1)^6, (G.3 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.3 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.3 * G.4^-1 * G.2 * G.4)^3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, (G.3 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.2 * G.1)^7, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.2 * G.4^-1)^6, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2 * G.1 * G.3)^3, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^6, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^6, (G.2 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, (G.3 * G.4^-1 * G.1 * G.4)^3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.4^-1 * G.2)^3, (G.1 * G.2 * G.1 * G.3)^3, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.3 * G.1)^3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.4^-1 * G.2)^7 ] Genus 92 action of group of order 1092 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-15 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-14 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-4 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-13 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-12 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^12 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4^13 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^16 * G.3 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.4^8 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-6 * G.3 * G.4^-5 * G.1 * G.4^12 * G.2 * G.1 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-46 * G.2 * G.1 * G.3 * G.4^-46 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-85 * G.1^2 * G.4^-8 ] Genus 92 action of group of order 372 via quadrangle group [ 2, 2, 2, 93 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-71 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 92 action of group of order 368 via quadrangle group [ 2, 2, 2, 184 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-46 * G.1 * G.4^-46 ] Genus 92 action of group of order 368 via quadrangle group [ 2, 2, 2, 184 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-84 * G.2 * G.4^-8 ] Genus 92 action of group of order 368 via quadrangle group [ 2, 2, 2, 184 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-71 * G.1 * G.2 * G.4^-20 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, (G.1 * G.3^-1 * G.4^-1)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2^2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.3, G.4^-1 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.3, G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 92 action of group of order 546 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.1 * G.4 * G.2 ] Largest orientation-preserving group for genus 92 has order 2184 ... group action with signature (0: +; [2,3,12]; {-}) ... group action with signature (0: +; [2,4,6]; {-}) Largest group with or without reflections for genus 92 has order 4368 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 92 has order 4368 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 92 has order 1092 ... group action with signature (0: +; [2,6,6]; {-}) ... group action with signature (0; +; [2,2,2,3]; {-}) Largest non-orientable group for non-orientable genus 93 has order 2184 ... group action with signature (0; +; [-]; {(2,4,6)}) ... group action with signature (0; +; [-]; {(2,3,12)}) Check total 1033 : 956 chiral, 77 reflexible, with 19 non-orientable quotient actions Genus 93 actions: Genus 93 action of group of order 768 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-32 * G.1 * G.3^8 * G.2^-1 * G.3^-7 ] Genus 93 action of group of order 768 via triangle group [ 2, 4, 96 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-78 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 93 action of group of order 768 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-78 * G.1 * G.3^11 * G.2^-1 * G.3^-6 ] Genus 93 action of group of order 768 via triangle group [ 2, 4, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-29 * G.1 * G.3^11 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 93 action of group of order 752 via triangle group [ 2, 4, 188 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-188 ] Genus 93 action of group of order 744 via triangle group [ 2, 4, 372 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-45 * G.1 * G.2^-1 * G.3^-140 ] Genus 93 action of group of order 672 via triangle group [ 2, 7, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-2 * G.2^3 * G.3^-2 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 93 action of group of order 576 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 93 action of group of order 576 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 93 action of group of order 576 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 93 action of group of order 576 via triangle group [ 2, 8, 18 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-7 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 93 action of group of order 576 via triangle group [ 2, 8, 18 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^-3 * G.1 * G.3^3 * G.2^-2 * G.3 * G.2 * G.3^-5 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-5 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^3 * G.2 * G.3^-2 * G.2 * G.3^5 * G.2^-1 * G.3^-1 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-7 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-12 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-28 * G.1 * G.3^20 * G.2 * G.3^-15 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-3 * G.1 * G.3^4 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-12 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-9 * G.1 * G.3^2 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^40 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 93 action of group of order 512 via triangle group [ 2, 8, 64 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-4 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^11 * G.2^-1 * G.3^-12 ] Genus 93 action of group of order 496 via triangle group [ 2, 8, 248 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^47 * G.2 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 93 action of group of order 496 via triangle group [ 2, 8, 248 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^48 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-11, G.1 * G.2^-5 * G.3^-1 * G.2^2 * G.3^-2 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-2 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-11, G.1 * G.2^-5 * G.3^-3 * G.2^2 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2, G.2^-11 ] Genus 93 action of group of order 506 via triangle group [ 2, 11, 22 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2, G.2^-11 ] Genus 93 action of group of order 480 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 93 action of group of order 480 via triangle group [ 2, 12, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^12, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 93 action of group of order 456 via triangle group [ 2, 12, 76 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-4 * G.1 * G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-9 ] Genus 93 action of group of order 434 via triangle group [ 2, 14, 217 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-4 * G.2^5 * G.3^-4, G.3^-11 * G.1 * G.3^4 * G.2^-1 * G.3^-15 ] Genus 93 action of group of order 384 via triangle group [ 2, 64, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-19 * G.3^4 * G.2^-6 * G.3^2 * G.2^-1 ] Genus 93 action of group of order 384 via triangle group [ 2, 64, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-27 * G.2^13 * G.3^-2 * G.2^20 * G.3^-1 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-92 * G.3 * G.2^-1 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.3^2 * G.2^-45 * G.3 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-6 * G.3^3 * G.2^-15 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^-6 * G.3^3 * G.2^-10 * G.3^2 * G.2^-1 * G.3^2 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-60 * G.2^35 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2 * G.3^-14 * G.2^11 * G.3^-4 * G.2 * G.3^-15 * G.2 * G.3^-1 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3 * G.2^-30 * G.3^3 * G.2^-13 ] Genus 93 action of group of order 384 via triangle group [ 2, 96, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-10 * G.2^12 * G.3^-4 * G.2^19 * G.3^-2 ] Genus 93 action of group of order 374 via triangle group [ 2, 187, 374 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^126 * G.2^-60 ] Genus 93 action of group of order 376 via triangle group [ 2, 188, 188 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^61 * G.3^-126 * G.2 ] Genus 93 action of group of order 372 via triangle group [ 2, 372, 372 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^60 * G.3^-125 * G.2 ] Genus 93 action of group of order 384 via triangle group [ 3, 8, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.3^-3 * G.1^-1 * G.2^-1 * G.3 * G.2, G.2^8 ] Genus 93 action of group of order 384 via triangle group [ 3, 8, 16 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^3, G.2^8 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^9 * G.2^-1 * G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-2)^2, G.3^15 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-5 * G.1^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^12 * G.2^-1 * G.3^-5 * G.1^-1 * G.2^-1 * G.1 * G.3^5 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-41 * G.1 * G.2 * G.3^-6 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^-12 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^9 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-4 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^6 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^-15 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-2)^2, G.3^-16 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^5 * G.2 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^38 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1^-1 * G.3 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-15 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^11 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^15 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^10 * G.2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^10 * G.2 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3, G.3^14 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3^4 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^11 * G.2 * G.1 * G.3^4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-4 * G.1^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^34 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^9 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-2)^2, G.3^9 * G.2 * G.3^-5 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^5 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-35 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-13 * G.1^-1 * G.3^3 * G.2 * G.3^-3 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-15 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^-1 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-12 * G.1 * G.3^4 * G.2 * G.3^-3 * G.1^-1 * G.3^3 * G.2 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2 * G.1^2 * G.3 * G.2^-1, G.3^13 * G.2 * G.3^-6 * G.1^-1 * G.3^4 ] Genus 93 action of group of order 384 via triangle group [ 4, 4, 48 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-2)^2, G.3^-10 * G.1^-1 * G.3^6 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 93 action of group of order 376 via triangle group [ 4, 4, 94 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-80 * G.1 * G.2 * G.3^-13 ] Genus 93 action of group of order 372 via triangle group [ 4, 4, 186 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-79 * G.1 * G.2^-1 * G.3^-13 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^46 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^46 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 736 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 552 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.4^-3 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 460 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-48 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^34 * G.3 * G.4^-1 * G.1 * G.4^-12 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-25 * G.1 * G.4^8 * G.1 * G.4^-15 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^22 * G.2 * G.4^-12 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^31 * G.3 * G.1 * G.4^5 * G.2 * G.4^11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-33 * G.3 * G.4^-5 * G.1 * G.2 * G.4^-9 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^15 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^14 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-5 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^13 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^5 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^13 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^5 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1^2 * G.4^-5 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^12 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^-12 * G.1 * G.4^-2 * G.1 * G.4^-10 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^5 * G.3 * G.4^-4 * G.2 * G.4^5 * G.1 * G.3 * G.2 * G.4^6 * G.3 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-10 * G.2 * G.4^5 * G.3 * G.4^-2 * G.1^2 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.3 * G.4^-1 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.4^-3 * G.1 * G.4 * G.2 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-10 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-5 * G.1 * G.4^9 * G.3 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^10 * G.2 * G.4^-8 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^10 * G.3 * G.4^-5 * G.2 * G.4^-2 * G.1 * G.2 * G.4^3 * G.2 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^5 * G.3 * G.4^-11 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^11 * G.2 * G.4^-1 * G.3 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1, G.4^-13 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-8 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^13 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^-12 * G.1 * G.4^-2 * G.1 * G.4^-10 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^5 * G.3 * G.4^-6 * G.1^2 * G.4^-1 * G.1 * G.4^-11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^14 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-11 * G.2 * G.1 * G.4 * G.3 * G.4^-11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-4 * G.1, G.4^6 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-5 * G.1 * G.4^7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^8 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-7 * G.1 * G.4^3 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.2 * G.4^4, G.4 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4^2 * G.1^2 * G.3 * G.1 * G.3 * G.4^-8 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^6 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^4 * G.3 * G.4^-3 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^14 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-5 * G.2 * G.4^-5 * G.1 * G.2 * G.4 * G.2 * G.4^11 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^7 * G.2 * G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-10 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.4^-6 * G.2 * G.1 * G.4^15 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^11 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^3 * G.2 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^9 * G.2 * G.4^-2 * G.3 * G.4^-9 * G.1 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.3 * G.4^-13 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^4 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-8 * G.1 * G.4^-2 * G.1 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, (G.2 * G.4^-4 * G.1 * G.4)^2, G.4^-1 * G.2 * G.4^4 * G.3 * G.4^-4 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^2 * G.2 * G.4^4 * G.3 * G.1 * G.3 * G.4^-5 * G.2 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^4 * G.3 * G.2 * G.4, G.4^4 * G.2 * G.4^-2 * G.1 * G.4^2 * G.1^2 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4, G.4^2 * G.3 * G.4^-5 * G.2 * G.4^-2 * G.1 * G.2 * G.4^3 * G.2 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4 * G.3 * G.4^-4, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^-5 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.4^-4 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^7 * G.3 * G.4^-2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^6 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^7 * G.2 * G.1 * G.4 * G.2 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-7 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-4 * G.1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.2 * G.4^2 * G.1 * G.3 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4 * G.1 * G.4^9 * G.3 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.2 * G.1 * G.4^5 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-5 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 * G.2 * G.4^-1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4, G.4^-3 * G.2 * G.4^2 * G.1 * G.3 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4, G.3 * G.4^-5 * G.2 * G.4^4 * G.3 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.2 * G.1 * G.4^5 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.2 * G.4^-5 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.2 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4^5 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^3 * G.3 * G.1 * G.4^-4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^4 * G.2 * G.1 * G.4 * G.2 * G.4^-4 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3, G.4^-1 * G.1 * G.4^5 * G.2 * G.4^-4 * G.1 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-5 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3, G.4^-5 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-19 * G.2 * G.4 * G.3 * G.4^-16 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^8 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^48 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-19 * G.1 * G.4^6 * G.2 * G.4^-2 * G.1 * G.4^4 * G.2 * G.4^-15 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^15 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-5 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^13 * G.3 * G.4^-1 * G.1^2 * G.4^-5 * G.1 * G.3 * G.1 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1^2 * G.4^-5 * G.1 * G.4^4 * G.2 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^12 * G.1 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.1 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.4^-5 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.2 * G.4^12 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^15 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-13 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1^2 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-17 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-10 * G.1 * G.2 * G.4^-1 * G.1^2 * G.4^-5 * G.1 * G.4^6 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^5 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-9 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.4^6 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^4 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.3 * G.2 * G.4^3 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^18 * G.1 * G.3 * G.1 * G.2 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-17 * G.2 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-12 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-8 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^34 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.2 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-42 * G.1^2 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-48 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^16 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^9 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-10 * G.1 * G.4^2 * G.2 * G.4^5 * G.1 * G.4^-7 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-34 * G.1 * G.4^4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^35 * G.3 * G.4^-6 * G.2 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^48 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^11 * G.1 * G.4^-1 * G.1 * G.4^3 * G.2 * G.1 * G.4^8 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^17 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^12 * G.2 * G.4^-5 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^35 * G.2 * G.3 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^48 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-34 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4 * G.3 * G.2 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4^4 * G.1 * G.3 * G.2 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4^5 * G.3 * G.4^-4 * G.1 * G.4^-1 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.2 * G.4^2 * G.1 * G.4^2 * G.3 * G.4^-5 * G.2 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-5 * G.1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^5 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.1 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.4^2 * G.3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 93 action of group of order 384 via quadrangle group [ 2, 2, 2, 48 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^6 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.1 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^19 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^19 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^17 * G.3 * G.4^-7 * G.2 * G.4 * G.3 * G.1^2 * G.2 * G.4^18 * G.3 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^40 * G.3 * G.1 * G.4^6 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^39 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.4^17 * G.2 * G.4^-1 * G.1 * G.4^13 * G.2 * G.4^-4 * G.1 * G.4^2 * G.2 * G.4^-6 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^19 * G.2 * G.4^-1 * G.1 * G.4^19 * G.2 * G.1 * G.4 * G.2 * G.4^-4 * G.1 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-94 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-86 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 93 action of group of order 376 via quadrangle group [ 2, 2, 2, 94 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-72 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 93 action of group of order 372 via quadrangle group [ 2, 2, 2, 186 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-46 * G.2 * G.3 * G.4^-46 ] Genus 93 action of group of order 372 via quadrangle group [ 2, 2, 2, 186 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-85 * G.1 * G.3 * G.4^-7 ] Genus 93 action of group of order 372 via quadrangle group [ 2, 2, 2, 186 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-72 * G.1 * G.2 * G.4^-20 ] Largest orientation-preserving group for genus 93 has order 768 ... group action with signature (0: +; [2,4,96]; {-}) Largest group with or without reflections for genus 93 has order 1536 ... group action with signature (0; +; [-]; {(2,4,96)}) Largest group with reflections for genus 93 has order 1536 ... group action with signature (0; +; [-]; {(2,4,96)}) Largest chiral group for genus 93 has order 736 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 94 has order 768 ... group action with signature (0; +; [-]; {(2,4,96)}) Check total 881 : 576 chiral, 305 reflexible, with 82 non-orientable quotient actions Genus 94 actions: Genus 94 action of group of order 2232 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 94 action of group of order 2232 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 94 action of group of order 840 via triangle group [ 2, 4, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-4)^2, (G.2 * G.3^-1)^6, G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 94 action of group of order 792 via triangle group [ 2, 4, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2 * G.3^-1)^6, G.3^-2 * G.1 * G.3^5 * G.2 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 94 action of group of order 760 via triangle group [ 2, 4, 190 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-190 ] Genus 94 action of group of order 752 via triangle group [ 2, 4, 376 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-46 * G.1 * G.2^-1 * G.3^-141 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 94 action of group of order 1116 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 ] Genus 94 action of group of order 744 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 94 action of group of order 744 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 744 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.2^-2 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 94 action of group of order 744 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 94 action of group of order 576 via triangle group [ 2, 6, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-14 * G.1 * G.3^11 * G.2^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 94 action of group of order 576 via triangle group [ 2, 6, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-58 * G.1 * G.3^19 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 94 action of group of order 576 via triangle group [ 2, 6, 96 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^74 * G.2 * G.3^-5 * G.1 * G.3^16 ] Genus 94 action of group of order 564 via triangle group [ 2, 6, 282 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^77 * G.2 * G.1 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^4 ] Genus 94 action of group of order 558 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 94 action of group of order 558 via triangle group [ 2, 9, 18 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.3^2 * G.2^-3 * G.3^4, G.3^2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, (G.2 * G.3^-3 * G.2)^2, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^10, (G.2 * G.3^-1 * G.2^3)^2 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, (G.2 * G.3^-3 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 94 action of group of order 620 via triangle group [ 2, 10, 10 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.2^10, (G.2 * G.3^-2 * G.2^2)^2 ] Genus 94 action of group of order 470 via triangle group [ 2, 10, 235 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-8 * G.1 * G.3^23 * G.2 * G.3^-9 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 94 action of group of order 504 via triangle group [ 2, 12, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-4 * G.1 * G.3^8 * G.2^-1 * G.3^-3 ] Genus 94 action of group of order 504 via triangle group [ 2, 12, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^3 * G.2^3 * G.1 * G.3^3 ] Genus 94 action of group of order 456 via triangle group [ 2, 12, 114 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^24 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-8 * G.1 * G.3^3 ] Genus 94 action of group of order 432 via triangle group [ 2, 18, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.2 * G.1 * G.3^11 * G.2 * G.3^-4 * G.1 * G.2 * G.3^-5 * G.1 * G.3 ] Genus 94 action of group of order 432 via triangle group [ 2, 18, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3^2 ] Genus 94 action of group of order 432 via triangle group [ 2, 18, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, (G.3 * G.2^-1 * G.3)^3, G.1 * G.3^3 * G.2^-1 * G.3^-4 ] Genus 94 action of group of order 432 via triangle group [ 2, 24, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 94 action of group of order 432 via triangle group [ 2, 24, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.3^2 ] Genus 94 action of group of order 432 via triangle group [ 2, 24, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^9 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 94 action of group of order 432 via triangle group [ 2, 24, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-2 * G.3^4 ] Genus 94 action of group of order 420 via triangle group [ 2, 30, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^-8 * G.3^-1 * G.2 * G.1, G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-5 ] Genus 94 action of group of order 420 via triangle group [ 2, 35, 35 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 396 via triangle group [ 2, 66, 66 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^-4 * G.3 * G.2^-2 * G.3^2 * G.2^-7 * G.3^4 * G.2^-1 * G.3 ] Genus 94 action of group of order 396 via triangle group [ 2, 66, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-29 * G.2^2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-4 * G.2 * G.3^-17 ] Genus 94 action of group of order 396 via triangle group [ 2, 66, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-30 * G.2^13 * G.3^-2 * G.2^19 * G.3^-2 ] Genus 94 action of group of order 378 via triangle group [ 2, 189, 378 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^127 * G.2^-60 * G.3 ] Genus 94 action of group of order 380 via triangle group [ 2, 190, 190 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^62 * G.3^-128 ] Genus 94 action of group of order 376 via triangle group [ 2, 376, 376 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^61 * G.3^-127 ] Genus 94 action of group of order 1116 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 94 action of group of order 1116 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 ] Genus 94 action of group of order 504 via triangle group [ 3, 4, 21 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 94 action of group of order 504 via triangle group [ 3, 4, 21 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1^-1 * G.3^3 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^-3 * G.2 * G.1 * G.3 * G.2^2 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2^2 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.1^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 94 action of group of order 465 via triangle group [ 3, 5, 15 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-2 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^6, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 94 action of group of order 558 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^6, (G.3^-1 * G.2)^3, G.1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^2 ] Genus 94 action of group of order 396 via triangle group [ 4, 4, 33 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1^-1 * G.3^5 ] Genus 94 action of group of order 380 via triangle group [ 4, 4, 95 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-5 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 * G.2 * G.3^-3 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 94 action of group of order 380 via triangle group [ 4, 4, 95 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^12 * G.2 * G.3^-2 * G.1 * G.3^4 ] Genus 94 action of group of order 380 via triangle group [ 4, 4, 95 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-81 * G.1 * G.2 * G.3^-13 ] Genus 94 action of group of order 376 via triangle group [ 4, 4, 188 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-80 * G.1 * G.2^-1 * G.3^-13 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 744 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-16 * G.2 * G.1 * G.3 * G.4^-16 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-8 * G.2 * G.4^9 * G.3 * G.4^-2 * G.1 * G.4^-13 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-12 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^8 * G.2 * G.4^-5 * G.1 * G.4^5 * G.2 * G.1 * G.4^13 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8 * G.3 * G.4^-6 * G.2 * G.4^-5 * G.1 * G.2 * G.4^2 * G.2 * G.4^8 * G.2 * G.4 * G.2 * G.4^2 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^13 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4^6 * G.2 * G.1 * G.4 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^5 * G.1 * G.3 * G.2 * G.4^5 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^6 ] Genus 94 action of group of order 396 via quadrangle group [ 2, 2, 2, 33 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.4^-4 * G.1, G.4^-9 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-8 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-4, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-11 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1 * G.3 * G.4^-4 * G.2, G.1 * G.3 * G.1 * G.4^10 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-6 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.4^5 * G.2 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^6 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.3 * G.4^-6 * G.1 * G.4^10 * G.2 * G.4^2 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.2 * G.1 * G.4^4 * G.3, G.2 * G.1 * G.2 * G.4^-2 * G.3 * G.4^-5 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.4 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-47 * G.2 * G.1 * G.3 * G.4^-47 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-87 * G.1^2 * G.4^-8 ] Genus 94 action of group of order 380 via quadrangle group [ 2, 2, 2, 95 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-73 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 94 action of group of order 376 via quadrangle group [ 2, 2, 2, 188 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-47 * G.1 * G.4^-47 ] Genus 94 action of group of order 376 via quadrangle group [ 2, 2, 2, 188 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-86 * G.2 * G.1^2 * G.4^-8 ] Genus 94 action of group of order 376 via quadrangle group [ 2, 2, 2, 188 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-73 * G.1 * G.2 * G.4^-20 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1)^6, G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.4 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.3 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.3^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, G.4 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2^2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.1^2 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-2 * G.3 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.4 * G.2 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-2 * G.3 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.3^2 * G.2^-1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.4 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 94 action of group of order 558 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Largest orientation-preserving group for genus 94 has order 2232 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 94 has order 2232 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with reflections for genus 94 has order 1680 ... group action with signature (0; +; [-]; {(2,4,35)}) Largest chiral group for genus 94 has order 2232 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 95 has order 744 ... group action with signature (0; +; [2]; {(2,4)}) Check total 741 : 664 chiral, 77 reflexible, with 12 non-orientable quotient actions Genus 95 actions: Genus 95 action of group of order 768 via triangle group [ 2, 4, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-78 * G.1 * G.3^9 * G.2^-1 * G.3^-8 ] Genus 95 action of group of order 768 via triangle group [ 2, 4, 192 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-192 ] Genus 95 action of group of order 760 via triangle group [ 2, 4, 380 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-47 * G.1 * G.2^-1 * G.3^-142 ] Genus 95 action of group of order 570 via triangle group [ 2, 6, 285 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-57 * G.1 * G.3^19 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 95 action of group of order 512 via triangle group [ 2, 8, 128 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-27 * G.1 * G.3^21 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-13 ] Genus 95 action of group of order 512 via triangle group [ 2, 8, 128 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^40 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^21 ] Genus 95 action of group of order 480 via triangle group [ 2, 12, 40 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3^5 ] Genus 95 action of group of order 480 via triangle group [ 2, 12, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 95 action of group of order 480 via triangle group [ 2, 12, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^12, G.1 * G.3^8 * G.2 * G.1 * G.2 * G.3^-5 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 95 action of group of order 480 via triangle group [ 2, 12, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-7 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-9 * G.1 * G.2^-1 * G.3^-9 ] Genus 95 action of group of order 456 via triangle group [ 2, 12, 228 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^22 * G.2 * G.3^-3 * G.1 * G.3^7 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 95 action of group of order 448 via triangle group [ 2, 16, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-6 * G.3^-1 * G.2 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^11 * G.2 * G.1 * G.2 * G.1 * G.3^9 * G.2^-1 * G.3^-2 ] Genus 95 action of group of order 448 via triangle group [ 2, 16, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^3 * G.1 * G.2^-1, G.3^-9 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 95 action of group of order 440 via triangle group [ 2, 20, 44 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^3 * G.1 * G.2^-3 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2^5, G.3^-2 * G.1 * G.3^3 * G.2 * G.1 * G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 95 action of group of order 418 via triangle group [ 2, 22, 209 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^9 * G.2 * G.3^-3 * G.1 * G.3^6 ] Genus 95 action of group of order 390 via triangle group [ 2, 78, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.2 * G.3^-1 * G.2^11 * G.3^-4 * G.2^20 * G.3^-2 ] Genus 95 action of group of order 382 via triangle group [ 2, 191, 382 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^128 * G.2^-62 ] Genus 95 action of group of order 384 via triangle group [ 2, 192, 192 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^63 * G.3^-128 * G.2 ] Genus 95 action of group of order 384 via triangle group [ 2, 192, 192 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-60 * G.2^33 * G.3^-2 ] Genus 95 action of group of order 380 via triangle group [ 2, 380, 380 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^62 * G.3^-127 * G.2 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-83 * G.1 * G.2 * G.3^-12 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^33 * G.2 * G.1^-1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^38 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1 * G.3 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^34 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^6 * G.2^-1 * G.1 * G.3^2 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^33 * G.2 * G.1^-1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-5 * G.1^-1 * G.3 ] Genus 95 action of group of order 384 via triangle group [ 4, 4, 96 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-35 * G.1^-1 * G.3^4 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-6 ] Genus 95 action of group of order 380 via triangle group [ 4, 4, 190 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-81 * G.1 * G.2^-1 * G.3^-13 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 752 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 564 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-96 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-88 * G.2 * G.1 * G.3 * G.4^-7 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-74 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-18 * G.2 * G.4 * G.3 * G.4^-16 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^8 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^37 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^6 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4 * G.2 * G.4^-19 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-14 * G.1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^35 * G.3 * G.1 * G.4^-12 * G.2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-24 * G.1 * G.4^-1 * G.1 * G.4^-23 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^31 * G.3 * G.1 * G.2 * G.4^16 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-33 * G.3 * G.4^-5 * G.1 * G.4^7 * G.2 * G.4^-2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-25 * G.1 * G.4^8 * G.1^2 * G.3 * G.1 * G.3 * G.4^-13 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^22 * G.2 * G.4^-11 * G.1 * G.2 * G.1 * G.4^13 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-16 * G.1 * G.4^-1 * G.1 * G.4^-15 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^19 * G.3 * G.1 * G.4^-12 * G.2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^7 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-12 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^8 * G.2 * G.4^-8 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^4 * G.3 * G.4^-13 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.4^8 * G.2 * G.4 * G.2 * G.4^2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^6 * G.2 * G.4^-7 * G.3 * G.4^-5 * G.1 * G.4^13 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.4^-5 * G.2 * G.4^2 * G.3 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4 * G.1 * G.4^7 * G.3 * G.1^2 * G.4^-1 * G.2 * G.4^6 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.4^7 * G.3 * G.1 * G.4 * G.1^2 * G.4 * G.3 * G.4^-5 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^8 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.1 * G.4 * G.2 * G.4^6 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-3 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-7 * G.2 * G.3 * G.1^2 * G.2 * G.4^6 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^8 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 * G.1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^2 * G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-4 * G.1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-5 * G.1 * G.2 * G.4^-2 * G.1 * G.4^4 * G.3 * G.4^2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-8 * G.1 * G.4^-5 * G.2 * G.3 * G.4^-2 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, (G.2 * G.4^-4 * G.1 * G.4)^2, G.2 * G.4^3 * G.3 * G.4^-5 * G.2 * G.1^2 * G.4^5 * G.3 * G.4^-1 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1, G.4^-3 * G.1 * G.4^4 * G.3 * G.1 * G.3 * G.4^-7 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^4 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 * G.1 * G.4 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.4^-4, G.4^2 * G.3 * G.4^-5 * G.2 * G.4^-2 * G.1 * G.4^6 ] Genus 95 action of group of order 384 via quadrangle group [ 2, 2, 2, 96 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-4 * G.1 * G.4 * G.3 * G.4^-4, G.4 * G.2 * G.4^-4 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^5 * G.3 * G.4 ] Genus 95 action of group of order 380 via quadrangle group [ 2, 2, 2, 190 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-47 * G.2 * G.3 * G.4^-47 ] Genus 95 action of group of order 380 via quadrangle group [ 2, 2, 2, 190 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-87 * G.1 * G.3 * G.4^-7 ] Genus 95 action of group of order 380 via quadrangle group [ 2, 2, 2, 190 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-74 * G.1 * G.2 * G.4^-20 ] Largest orientation-preserving group for genus 95 has order 768 ... group action with signature (0: +; [2,4,192]; {-}) Largest group with or without reflections for genus 95 has order 1536 ... group action with signature (0; +; [-]; {(2,4,192)}) Largest group with reflections for genus 95 has order 1536 ... group action with signature (0; +; [-]; {(2,4,192)}) Largest chiral group for genus 95 has order 752 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 96 has order 752 ... group action with signature (0; +; [-]; {(2,2,2,4)}) Check total 402 : 316 chiral, 86 reflexible, with 31 non-orientable quotient actions Genus 96 actions: Genus 96 action of group of order 3420 via triangle group [ 2, 3, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 96 action of group of order 3420 via triangle group [ 2, 3, 9 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 96 action of group of order 3420 via triangle group [ 2, 3, 9 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.2 * G.3^-4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 ] Genus 96 action of group of order 792 via triangle group [ 2, 4, 99 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-80 * G.1 * G.3^10 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 96 action of group of order 776 via triangle group [ 2, 4, 194 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-194 ] Genus 96 action of group of order 768 via triangle group [ 2, 4, 384 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-48 * G.1 * G.2^-1 * G.3^-143 ] Genus 96 action of group of order 588 via triangle group [ 2, 6, 98 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-60 * G.1 * G.3^17 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-17 ] Genus 96 action of group of order 528 via triangle group [ 2, 8, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-12 * G.1 * G.3^7 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 96 action of group of order 528 via triangle group [ 2, 8, 66 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-41 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-17 ] Genus 96 action of group of order 600 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2^10, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 96 action of group of order 600 via triangle group [ 2, 10, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^10, G.3^-2 * G.1 * G.3^3 * G.2^-1 * G.3^-6 ] Genus 96 action of group of order 600 via triangle group [ 2, 10, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-2, G.2^10, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^26 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^36 * G.2^-1 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-2, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-2, G.3^3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 96 action of group of order 500 via triangle group [ 2, 10, 50 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^10, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-2, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 96 action of group of order 480 via triangle group [ 2, 10, 240 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^-14 * G.1 * G.3^20 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-9 ] Genus 96 action of group of order 476 via triangle group [ 2, 14, 34 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^14, G.3^-7 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-18 ] Genus 96 action of group of order 448 via triangle group [ 2, 14, 224 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-4 * G.2^5 * G.3^-4, G.3^-1 * G.1 * G.3^14 * G.2 * G.3^-4 * G.1 * G.3^8 * G.2^-1 * G.3^-3 ] Genus 96 action of group of order 468 via triangle group [ 2, 18, 26 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-2 * G.3 * G.2 * G.1 * G.3 * G.2^4 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-4, G.3^15 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^2 ] Genus 96 action of group of order 416 via triangle group [ 2, 26, 208 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-13 * G.3^4 * G.2^-5 * G.3^4 ] Genus 96 action of group of order 420 via triangle group [ 2, 30, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^7 * G.3^-1 * G.2 * G.3^-1, G.3^-5 * G.1 * G.3^2 * G.2 * G.3^-6 ] Genus 96 action of group of order 408 via triangle group [ 2, 34, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-21 * G.3^4 * G.2^-5 * G.3^4 ] Genus 96 action of group of order 400 via triangle group [ 2, 50, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-12 * G.2^12 * G.3^-4 * G.2^21 ] Genus 96 action of group of order 408 via triangle group [ 2, 51, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-4 * G.3^3 * G.2^-1 * G.3 ] Genus 96 action of group of order 392 via triangle group [ 2, 98, 196 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-62 * G.2^33 * G.3^-2 ] Genus 96 action of group of order 396 via triangle group [ 2, 99, 99 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-95 * G.3 * G.2^-1 ] Genus 96 action of group of order 390 via triangle group [ 2, 130, 195 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-28 * G.2^13 * G.3^-2 * G.2^19 * G.3^-1 * G.2 ] Genus 96 action of group of order 386 via triangle group [ 2, 193, 386 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^129 * G.2^-62 * G.3 ] Genus 96 action of group of order 388 via triangle group [ 2, 194, 194 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^64 * G.3^-130 ] Genus 96 action of group of order 384 via triangle group [ 2, 384, 384 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^63 * G.3^-129 ] Genus 96 action of group of order 588 via triangle group [ 3, 3, 98 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^4 * G.2^-1 * G.3^-6 * G.1^-1 * G.3^5 ] Genus 96 action of group of order 588 via triangle group [ 3, 3, 98 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-5 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 96 action of group of order 579 via triangle group [ 3, 3, 193 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^2 * G.2^-1 * G.3^-4 * G.1^-1 * G.2^-1 * G.3^-5 * G.1^-1 * G.3^3 ] Genus 96 action of group of order 579 via triangle group [ 3, 3, 193 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^3 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-4 * G.1^-1 * G.3^4 ] Genus 96 action of group of order 600 via triangle group [ 3, 4, 10 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^10 ] Genus 96 action of group of order 388 via triangle group [ 4, 4, 97 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^-2 * G.1 * G.2^-1 * G.3^4 ] Genus 96 action of group of order 388 via triangle group [ 4, 4, 97 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^7 * G.2 * G.3^-3 * G.1 * G.3^2 ] Genus 96 action of group of order 388 via triangle group [ 4, 4, 97 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^84 * G.2 * G.1 * G.3^12 ] Genus 96 action of group of order 384 via triangle group [ 4, 4, 192 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^-83 * G.1 * G.2^-1 * G.3^-12 ] Genus 96 action of group of order 456 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 96 action of group of order 456 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.2^-1 * G.3^2 * G.2^-1 * G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 96 action of group of order 456 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 ] Genus 96 action of group of order 456 via triangle group [ 4, 6, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-2 * G.3 * G.2^-2 ] Genus 96 action of group of order 388 via quadrangle group [ 2, 2, 2, 97 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-48 * G.2 * G.1 * G.3 * G.4^-48 ] Genus 96 action of group of order 388 via quadrangle group [ 2, 2, 2, 97 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-89 * G.1^2 * G.4^-8 ] Genus 96 action of group of order 388 via quadrangle group [ 2, 2, 2, 97 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^77 * G.1^2 * G.4^20 ] Genus 96 action of group of order 384 via quadrangle group [ 2, 2, 2, 192 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-48 * G.1 * G.4^-48 ] Genus 96 action of group of order 384 via quadrangle group [ 2, 2, 2, 192 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-88 * G.2 * G.1^2 * G.4^-8 ] Genus 96 action of group of order 384 via quadrangle group [ 2, 2, 2, 192 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-75 * G.1 * G.2 * G.4^-20 ] Largest orientation-preserving group for genus 96 has order 3420 ... group action with signature (0: +; [2,3,9]; {-}) Largest group with or without reflections for genus 96 has order 6840 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest group with reflections for genus 96 has order 6840 ... group action with signature (0; +; [-]; {(2,3,9)}) Largest chiral group for genus 96 has order 500 ... group action with signature (0: +; [2,10,50]; {-}) Largest non-orientable group for non-orientable genus 97 has order 3420 ... group action with signature (0; +; [-]; {(2,3,9)}) Check total 52 : 8 chiral, 44 reflexible, with 15 non-orientable quotient actions Genus 97 actions: Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-2 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 2304 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^12, G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^5 * G.2^-1 * G.3^-6, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^2 * G.3^-4 * G.1 * G.3 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^2 * G.3^-3 * G.1 * G.3^2, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.1 * G.3^5 ] Genus 97 action of group of order 1536 via triangle group [ 2, 3, 24 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-4 ] Genus 97 action of group of order 1440 via triangle group [ 2, 3, 30 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^5 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^6 ] Genus 97 action of group of order 3840 via triangle group [ 2, 4, 5 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 3840 via triangle group [ 2, 4, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 3840 via triangle group [ 2, 4, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-2 * G.1 * G.2 * G.3^-2, G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 2304 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-2 ] Genus 97 action of group of order 2304 via triangle group [ 2, 4, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4 ] Genus 97 action of group of order 2304 via triangle group [ 2, 4, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^6, G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1792 via triangle group [ 2, 4, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, (G.2 * G.3^-2)^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 97 action of group of order 1792 via triangle group [ 2, 4, 7 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, (G.2 * G.3^-1)^4, G.3^2 * G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2 * G.3^-2 * G.2 * G.3^-3 * G.2 * G.1 ] Genus 97 action of group of order 1792 via triangle group [ 2, 4, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 97 action of group of order 1280 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^10, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 97 action of group of order 1280 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^10, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1280 via triangle group [ 2, 4, 10 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^10, (G.2 * G.3^-2)^4, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.2^-1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^3 ] Genus 97 action of group of order 1152 via triangle group [ 2, 4, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12 ] Genus 97 action of group of order 1152 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^12 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-2)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^5 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.2 * G.3^-2)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.3^-6 * G.1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.3^4 * G.2^-1 * G.3^3)^2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2)^4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2, (G.2 * G.3^-2)^4, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.3^-5 * G.1 * G.3^7 * G.2^-1 * G.3^-3 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.2, G.3^-2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4, (G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, (G.2^-1 * G.3 * G.2^-1 * G.3^3 * G.2^-1 * G.3)^2, G.3^-6 * G.1 * G.3^7 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^3, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^6 * G.2^-1 * G.3^-2 * G.1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-2)^4, G.1 * G.3 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.2, G.3^-5 * G.1 * G.3^7 * G.2^-1 * G.3^-3 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-2)^4, G.3^2 * G.2^-1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^-6 * G.2 * G.1 * G.3^6 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^4 * G.2^-1 * G.3^5 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-2)^4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 97 action of group of order 1024 via triangle group [ 2, 4, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 97 action of group of order 960 via triangle group [ 2, 4, 20 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2 * G.2 * G.3^-1)^2, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1 ] Genus 97 action of group of order 960 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-1)^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3^-3 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 896 via triangle group [ 2, 4, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2, G.3^-5 * G.1 * G.3^8 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 832 via triangle group [ 2, 4, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-36 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 97 action of group of order 800 via triangle group [ 2, 4, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-82 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 97 action of group of order 784 via triangle group [ 2, 4, 196 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-196 ] Genus 97 action of group of order 776 via triangle group [ 2, 4, 388 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-49 * G.1 * G.2^-1 * G.3^-144 ] Genus 97 action of group of order 1920 via triangle group [ 2, 5, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1920 via triangle group [ 2, 5, 5 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, (G.2 * G.3^-1)^6, G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 1920 via triangle group [ 2, 5, 5 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.3^-2 * G.1 * G.2 * G.3^-2, G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.1, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-1 * G.2)^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.2^2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.3 * G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, (G.3 * G.2^-1 * G.3)^3 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.2^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-1 * G.2 * G.3^-2 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.3^2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2, (G.2 * G.3^-1 * G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.3^-1 * G.2^2 * G.3^-1)^3 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2^-2 * G.3)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-2, G.3 * G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2^-2 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^-1 * G.3^2 * G.2^3 * G.3^-2 * G.2 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2^2 * G.3^-2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2 * G.3^-2 * G.2)^2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.3^-1 * G.2^2 * G.3^-1)^3, (G.2 * G.3^-2)^4 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.2 * G.3^-2 * G.2 * G.3^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-1 * G.3^2, G.3 * G.2 * G.1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 97 action of group of order 1008 via triangle group [ 2, 6, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.3^2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 864 via triangle group [ 2, 6, 9 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 97 action of group of order 864 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.1 * G.2^-2 * G.3^2 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 97 action of group of order 864 via triangle group [ 2, 6, 9 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^-4 * G.1 * G.2 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^3 * G.2^2 * G.1 * G.3^2, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-5)^2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^3, G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^2 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.1 * G.3^3, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-3 * G.3^-3 * G.2^2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-3 * G.3^-3 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-3 * G.2 * G.3^-1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^-2 * G.2 * G.3^-2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2)^4, (G.2 * G.3^-4 * G.2)^2 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3^2, G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-4, G.3 * G.2^-2 * G.3 * G.2^3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 2, 6, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-4, (G.2 * G.3^-1 * G.2)^4 ] Genus 97 action of group of order 720 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3 * G.2^-1 * G.3 * G.2^3 * G.3^-1 * G.2 * G.3^-1 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 720 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 97 action of group of order 672 via triangle group [ 2, 6, 21 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 ] Genus 97 action of group of order 648 via triangle group [ 2, 6, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 648 via triangle group [ 2, 6, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 648 via triangle group [ 2, 6, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-1 * G.1 * G.3^4 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-13 ] Genus 97 action of group of order 600 via triangle group [ 2, 6, 75 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.3^-6 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 97 action of group of order 594 via triangle group [ 2, 6, 99 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-8 * G.1 * G.3^13 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 97 action of group of order 594 via triangle group [ 2, 6, 99 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-11 * G.1 * G.3 * G.2 * G.1 * G.3^8 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 97 action of group of order 594 via triangle group [ 2, 6, 99 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-59 * G.1 * G.3^14 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 97 action of group of order 582 via triangle group [ 2, 6, 291 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-57 * G.1 * G.3^21 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 97 action of group of order 896 via triangle group [ 2, 7, 7 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, G.1 * G.2^-2 * G.3 * G.2^-3 * G.3^-3 * G.2 * G.3^-2 ] Genus 97 action of group of order 896 via triangle group [ 2, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 896 via triangle group [ 2, 7, 7 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3^-3 * G.1 * G.2 * G.3^-3, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^6 * G.2^3 * G.1 * G.3^5 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.1 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^3 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.2^8, G.2^-1 * G.3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.3^6 ] Genus 97 action of group of order 576 via triangle group [ 2, 8, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^3 ] Genus 97 action of group of order 640 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 640 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^10, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 97 action of group of order 640 via triangle group [ 2, 10, 10 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^10, (G.2 * G.3^-2 * G.2^2)^2, (G.2 * G.3^-3 * G.2)^2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.2^2 * G.1 * G.3 * G.2^2 * G.1 * G.3^3, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.3^2 * G.2^-4 * G.3^-1 * G.2 * G.1 * G.3^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.2^-2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12, (G.2 * G.3^-1 * G.2^4)^2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^12, G.2^2 * G.3^-1 * G.2^4 * G.3^-3 * G.2^2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^2 * G.2^3 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3 * G.2^-5 * G.3^-2 * G.1 * G.3^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2^2, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^12, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2^12, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.3^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1)^4, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^12, G.3^-12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-3)^2, G.3^-12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.2^12, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^12 ] Genus 97 action of group of order 576 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.2^12, G.3^-12 ] Genus 97 action of group of order 480 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.1 * G.2^-1 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-5 ] Genus 97 action of group of order 480 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^12, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-2 * G.1 * G.3^2 ] Genus 97 action of group of order 480 via triangle group [ 2, 12, 60 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3^4 * G.2^-1 * G.3^-3 * G.1 * G.3 ] Genus 97 action of group of order 480 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-2 * G.2 * G.3^-1 * G.2, G.2^15 ] Genus 97 action of group of order 480 via triangle group [ 2, 15, 30 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.2^15 ] Genus 97 action of group of order 480 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-3 * G.2, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-3 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 480 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-1 * G.2^4, G.2^15 ] Genus 97 action of group of order 480 via triangle group [ 2, 15, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.3^-1 * G.2 * G.3^-2 * G.2^5 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-3, G.2^2 * G.3^-2 * G.2^7 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2^3 * G.3^-1 * G.2^6 * G.3^-1 * G.2^3 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.3^2 * G.2^-1 * G.3 * G.2^-8 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^2 * G.3^-1 * G.2^4 * G.3^-1 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-1 * G.3 * G.2^-8 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-2 * G.3^-1 * G.2^4 * G.1 * G.2^-6 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.2^3 * G.3^-1 * G.2^6 * G.3^-1 * G.2^3 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2^2)^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2, G.3 * G.2^-3 * G.3 * G.2^-11 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, (G.2^-3 * G.3^5)^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^4 * G.3^-3 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, (G.2^-4 * G.3 * G.2^-3)^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-3 * G.3^2 * G.2^-1 * G.3^2 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1, (G.2^-5 * G.3 * G.2^-2)^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3 * G.2^-5 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^-6 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2^-5 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-6 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-9 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-8 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2^-6 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-6 * G.3^-1 * G.1 * G.2^-1 * G.3^2, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2 * G.1 * G.2^-3 * G.3 * G.2^11 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-10 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^2 * G.2^-5 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^5 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3, G.2^-6 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-2 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-2 * G.3^-4 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-3)^2, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-3)^2, G.2^-6 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-5 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.3 * G.2^-5 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-1, G.1 * G.3^2 * G.2^-2 * G.3^-1 * G.2 * G.3^-2, G.2 * G.1 * G.2^-4 * G.3 * G.2^-2 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-6 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.2^-6 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-5 * G.3^-2 * G.2^2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2 * G.2^-2 * G.3^-3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2^2)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3 * G.2^5 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-5 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-4, G.2^-6 * G.3^-2 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.2^2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^2, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 2, 16, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.3, G.1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 448 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-7 ] Genus 97 action of group of order 448 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-10 * G.2^2 * G.1 * G.3^2 * G.2^-1 * G.3^-15 ] Genus 97 action of group of order 448 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-4 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^9 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-13 * G.1 ] Genus 97 action of group of order 448 via triangle group [ 2, 16, 112 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^5 * G.3^-1 * G.2 * G.3^-1, G.3^-10 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-7 ] Genus 97 action of group of order 480 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 480 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.2 * G.3^-1 * G.2^3)^2, (G.2 * G.3^-4)^2 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3^3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-11 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^-1 * G.3^2 * G.2^-2 * G.3^4 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-11 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-11 * G.3^4 * G.2^-5 * G.3^4 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-10 * G.3^-1 * G.2 * G.1, G.3^9 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^9 * G.2 * G.3^-2 * G.1 * G.3^6 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-2 * G.2^4 * G.3^-4 * G.2 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^2 * G.3^-1 * G.2^4 * G.3^-5 ] Genus 97 action of group of order 432 via triangle group [ 2, 24, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.2^-10 * G.3^-1 * G.2 * G.1, G.3^-1 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 97 action of group of order 448 via triangle group [ 2, 28, 28 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-3 * G.2, G.2^2 * G.3^-1 * G.2^12 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 448 via triangle group [ 2, 28, 28 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2 * G.3^-2, G.2^4 * G.3^-10 * G.2^2 * G.3^-1 * G.2^7 * G.3^-2 * G.2 * G.3^-1 ] Genus 97 action of group of order 448 via triangle group [ 2, 28, 28 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2^3 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-3 * G.2 * G.3^-1 * G.2^5 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3 ] Genus 97 action of group of order 432 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-23 * G.3^4 * G.2^-5 * G.3^4 ] Genus 97 action of group of order 432 via triangle group [ 2, 36, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.2^-3 * G.3^14 * G.2^-1 * G.3^4 * G.2^-4 * G.3 * G.2^-2 * G.3 * G.2^-6 ] Genus 97 action of group of order 408 via triangle group [ 2, 51, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-51 ] Genus 97 action of group of order 416 via triangle group [ 2, 52, 52 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^36 * G.3^-1 * G.2^10 * G.3^-2 ] Genus 97 action of group of order 400 via triangle group [ 2, 100, 100 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-64 * G.2^35 ] Genus 97 action of group of order 390 via triangle group [ 2, 195, 390 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^130 * G.2^-64 ] Genus 97 action of group of order 392 via triangle group [ 2, 196, 196 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^65 * G.3^-130 * G.2 ] Genus 97 action of group of order 388 via triangle group [ 2, 388, 388 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^64 * G.3^-129 * G.2 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, (G.1 * G.3 * G.2)^4 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 97 action of group of order 1152 via triangle group [ 3, 3, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-4 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3^3 * G.2 * G.1^-1, G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-3 * G.1^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^-2 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 3, 3, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 ] Genus 97 action of group of order 720 via triangle group [ 3, 3, 15 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.1, G.3^-2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-3 ] Genus 97 action of group of order 1152 via triangle group [ 3, 4, 4 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 1152 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 ] Genus 97 action of group of order 1152 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2, G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1, (G.1^-1 * G.3^2 * G.2)^2 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-2 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, (G.1^-1 * G.3^2 * G.2)^2, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^6, (G.1^-1 * G.3^2 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 768 via triangle group [ 3, 4, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1, G.3^-12 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1, G.3^-12 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^4, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.3^-4 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2, G.2^-1 * G.3^-2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2, (G.1 * G.3^2 * G.2^-1 * G.3^-1)^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^4, (G.1 * G.3^2 * G.2 * G.3^-1)^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^3 * G.2, (G.1 * G.3^2 * G.2^-1 * G.3^-1)^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, (G.3^-1 * G.2)^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-2 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, (G.3^-1 * G.1^-1 * G.2^-1)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-2, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.2^-1 * G.3 * G.2^-3 * G.1^-1 * G.2^-2 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3 * G.2^2 * G.1^-1 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^6, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2, (G.2 * G.1^-1 * G.3)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1 * G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3^-1 * G.2^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-2 * G.3^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^2 * G.3^-1, (G.2 * G.1^-1 * G.3)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3, (G.2 * G.1^-1 * G.3)^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2^2 * G.1^-1 * G.2^3, G.2 * G.3^-2 * G.1^-1 * G.2 * G.3^-2, (G.1 * G.3 * G.2)^4 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2^2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-2 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-2 * G.3^-1, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.2 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2, G.3^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.3^-1 * G.2, G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3^6 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.3^-2 * G.2^2 * G.1^-1 * G.3 * G.2^3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.3^2, G.2^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2^2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, G.3^6, G.2 * G.3^-2 * G.1^-1 * G.2^-2 * G.3, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 504 via triangle group [ 3, 7, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, G.2^-7, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, (G.1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 97 action of group of order 504 via triangle group [ 3, 7, 7 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^-7, G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 504 via triangle group [ 3, 7, 7 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3, G.2^-7, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 97 action of group of order 432 via triangle group [ 3, 9, 9 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, (G.1^-1 * G.2^-1 * G.3^-1)^4 ] Genus 97 action of group of order 432 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 432 via triangle group [ 3, 9, 9 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^-9, G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.1^-1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-2 * G.2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1 * G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.2 * G.3^-1 * G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.1^-1 * G.3 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 640 via triangle group [ 4, 4, 5 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2^-1 * G.1^-1 * G.3^2, (G.1 * G.3^-2 * G.2)^2, (G.1 * G.3^-1)^4, G.1^-1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3^-2 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^6, (G.1 * G.2^-1)^4, (G.1^-1 * G.3^2 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^6, (G.1 * G.2^-1)^4, (G.1 * G.3^2 * G.2^-1)^2, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^6, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^6, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 97 action of group of order 576 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^6, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3, (G.1 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.1, G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.1^-1, G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-2 * G.1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.3^-1 * G.2 * G.1^2 * G.3^3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.2^-1)^4, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1^-1 * G.3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-3 * G.2 * G.1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.1 * G.2^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.2^-1)^4, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^8, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3^2 * G.2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^8, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3^2 * G.2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^8, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.1 * G.3 * G.2 * G.1^-2 * G.3^2 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^8, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^8, (G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2)^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, (G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2)^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.2^-1)^4, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.2^-1)^4, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^2 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^2 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, (G.1^-1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^8, G.3^-2 * G.1 * G.3^-1 * G.2 * G.1 * G.3^-3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2^-2 * G.3^-2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1^-1, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-2 * G.1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2^-2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, (G.2 * G.3^-1)^4, G.3^8, G.1^-1 * G.3^3 * G.2 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.3 * G.2^-1 * G.3^2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, (G.2 * G.3^-3)^2, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.3^-1 * G.1^-2 * G.3^2 * G.1^-1, G.3^8, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^2 * G.3^2 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.1^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, (G.2 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2^-2 * G.1 * G.3^-3, G.3^-3 * G.2 * G.1 * G.3^-1 * G.1 * G.2^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^8, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-2)^2, (G.2 * G.3^-1)^4, G.3^8, G.3^-2 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1 * G.2)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.1^-1, (G.1 * G.3^-1)^4, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.1^-1 * G.2^-1 * G.3^-2 * G.1^-1 * G.3^2 * G.1^-1 * G.3 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.2^-1 * G.3^2 * G.2^-1 * G.1 * G.3^2 * G.1^-1, G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, (G.2 * G.3^-1)^4, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.3^2 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2, G.3 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.1 * G.3, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1, (G.2 * G.3^-1)^4, G.3^8, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1 * G.2^-1 * G.1 * G.3^2, (G.1 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1)^4, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-3, G.3^2 * G.2^-2 * G.1 * G.3^-2 * G.1^-1, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^2, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.3 * G.1^-1, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.3^-2 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, (G.1 * G.3^-3)^2, G.3^8 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^2, (G.1 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1^-1 * G.2 * G.1^2 * G.3^3 * G.1^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.1 * G.3^-3)^2, G.3^8, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.2 * G.3^-2)^2, (G.1 * G.3^-1)^4, G.3^8, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.3^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.3^-1)^4, (G.2 * G.3^-1)^4, G.3^8, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.3^2 * G.2^2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.3^-2 * G.1^2 * G.3^3 * G.2^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^4, G.3^8, G.3^-1 * G.1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-1 * G.3^2, G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3^-1 * G.1 ] Genus 97 action of group of order 512 via triangle group [ 4, 4, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, (G.1 * G.3^-1 * G.2)^2, G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^-2 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-2 * G.1 * G.3^-1)^2 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2, G.1^-1 * G.2 * G.3^-2 * G.1^-1 * G.2^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2, (G.1 * G.3^-2 * G.1 * G.3^-1)^2 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^-3, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, (G.2 * G.3^-2)^2, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1 ] Genus 97 action of group of order 480 via triangle group [ 4, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, (G.1 * G.3^-2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2 ] Genus 97 action of group of order 448 via triangle group [ 4, 4, 14 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3 * G.1^-1, G.3^8 * G.2^-1 * G.1^-1 * G.3^5 ] Genus 97 action of group of order 416 via triangle group [ 4, 4, 26 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^16 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 97 action of group of order 416 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.2^-1 * G.3^-4 * G.1^-1 * G.3^5 ] Genus 97 action of group of order 416 via triangle group [ 4, 4, 26 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-5 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 97 action of group of order 400 via triangle group [ 4, 4, 50 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-38 * G.1^-1 * G.3 * G.2^-1 * G.3^-10 ] Genus 97 action of group of order 400 via triangle group [ 4, 4, 50 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^5 * G.1^-1 * G.3^5 ] Genus 97 action of group of order 400 via triangle group [ 4, 4, 50 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-2 * G.2 * G.3^-5 * G.1 * G.3^-6 ] Genus 97 action of group of order 392 via triangle group [ 4, 4, 98 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^82 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3^14 ] Genus 97 action of group of order 388 via triangle group [ 4, 4, 194 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^84 * G.2 * G.1^-1 * G.3^12 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3)^4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^8 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4)^2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^8 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, (G.2 * G.4^-1)^8 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^8 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^6, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.2 * G.4^-1 * G.2 * G.4)^3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1 * G.2 * G.4)^3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 1152 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^8, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^8, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^24 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^24 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^24 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^24 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^48 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^16 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^6, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^6, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^16 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^48 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.2)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.3)^4, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^2 * G.2 * G.4 * G.1 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.3 * G.1)^3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.4^-1 * G.2)^3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^48 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^16 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, (G.1 * G.4 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3)^4, G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, (G.1 * G.4 * G.3)^4, G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.2 * G.4^-1 * G.2 * G.4)^3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^6, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4^-2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^6, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^24 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 768 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^2 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-5, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-5, G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-2 * G.1 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-5, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-5, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.1 * G.3)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-5, (G.1 * G.4 * G.2 * G.4^-2 * G.2)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2)^2 ] Genus 97 action of group of order 640 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-5, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^48 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4^3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, (G.1 * G.3)^16 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.3 * G.4^-2 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, (G.1 * G.3)^24 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^24 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^24 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^6, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^2 * G.2 * G.3 * G.2 * G.4^-2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.4 * G.2 * G.4)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.3 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 * G.2 * G.4^3 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4^2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^2 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, (G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^6, G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.2)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, (G.1 * G.2)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2 * G.1 * G.3)^3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^6, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-2 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.3 * G.1 * G.3 * G.1 * G.4)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, (G.1 * G.3)^12 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.3)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3)^6, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, (G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4)^2, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.1, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.2)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^6, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.1 * G.4^2 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-3 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3)^6, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-2 * G.2 * G.3 * G.2 * G.4^-2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.4^2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, G.2 * G.4^-3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^2 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, (G.1 * G.2)^6, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.1 * G.2)^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.4^2 * G.3)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.1 * G.2)^6, G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-1 * G.1 * G.4^2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1, (G.1 * G.2)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^6, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.2)^4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.2 * G.4^-3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.3)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4^-1)^4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, (G.1 * G.4^3 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.4 * G.2 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4^2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.4 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, (G.2 * G.1)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, (G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^2 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.4^8, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.2)^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^8, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^8, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-2)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, (G.1 * G.3)^16 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2)^8, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2, G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^8, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.3 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, (G.1 * G.3 * G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^2 * G.1 * G.4^2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^8, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^8, G.4 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^8, G.4^2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^8, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2, G.4 * G.3 * G.2 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^8, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^8, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^8, G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, (G.2 * G.4^-1)^4, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4^8, G.4 * G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.4 * G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, G.4^8, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4^-1)^4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^8, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^8, G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^8, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.4^-4 * G.2 * G.1 * G.4^3 * G.3, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^8, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3)^2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^8, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.4^-1)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^8, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^8, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^8, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 512 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, (G.1 * G.3)^12 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.2)^6, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, (G.1 * G.3)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, (G.1 * G.3)^12 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, (G.1 * G.3)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3)^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^10, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^10, G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^10, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^10, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^10, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^10, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^10, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^10, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^10, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, (G.1 * G.2)^6 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.4^2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^10, G.4 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^10, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^10, G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^10, G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.4^-1 * G.2)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.4^-2 * G.1 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.4^-1 * G.2)^3, G.4^10, G.4^2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1)^3, (G.1 * G.2)^4, G.4^10, G.4^-1 * G.2 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.4^-1 * G.2)^3, G.4^10, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^10, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^10, G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^10, G.4^-1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3, G.4^10, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^3 * G.3 * G.2 * G.4^-4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.3 * G.1 * G.4^-4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.3)^4, G.4^10, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.4^3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^10, G.2 * G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^10, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^10, G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4^10 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^10 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^10, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.3 * G.1)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.4^-1 * G.2)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^10 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^10, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^10, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.3 * G.4^-3 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^10, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, (G.4^-1 * G.2)^5 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^5, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^5, (G.2 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.3)^4, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^10, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^10 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-3 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^10, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, (G.3 * G.1)^5, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.2)^4, G.4^10, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.2)^4, G.4^10, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^10, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^10, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4^10, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^10, (G.1 * G.3)^6, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-3 * G.1 * G.3 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^3 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^10, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^10, (G.1 * G.2)^6, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^10, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^10, (G.1 * G.2)^6, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.4^10, (G.1 * G.3)^6, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 97 action of group of order 480 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^3 * G.3 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-8 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5, G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8 * G.3 * G.2 * G.1 * G.4^5, (G.1 * G.3)^8 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.1^2 * G.4 * G.3 * G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.4^-1 * G.2 * G.4^6 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^14, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-8 * G.2 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.4^-6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.4^7 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-8 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-7 * G.1 * G.3 * G.1 * G.3 * G.4^-5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-7 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 448 via quadrangle group [ 2, 2, 2, 14 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^6 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.3 * G.4^-1 * G.2 * G.4)^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4^3 * G.1 * G.4 * G.1 * G.4^5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4, G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^18, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^7 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-5 * G.1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3, G.1 * G.4^6 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^4 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4^-1 * G.1 * G.4)^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4 * G.2 * G.1 * G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.2 * G.4^3 * G.1 * G.4 * G.1^2 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.4^-5 * G.2 * G.4^6 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^2 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^18, (G.1 * G.3)^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^8 * G.3 * G.1^2 * G.4^-1 * G.1 * G.4^-8 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^2 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.1 * G.4^7 * G.3 * G.1 * G.3 * G.1^2 * G.4^-8 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2)^6, G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4^3 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-4 * G.1 * G.3 * G.4^-6 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-11 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^18, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^9 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^6 * G.3 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-6 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-5, (G.1 * G.3)^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.4^3 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.1 * G.4^3 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.3 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2, G.4^5 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-8 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^3 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.4^6 * G.1 * G.4 * G.1^2 * G.3 * G.4^-8 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^2 * G.1 * G.4^2 * G.3 * G.4^-4 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4^-11 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.4^-2 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^18, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-2 * G.3 * G.1 * G.4^5 * G.1^2 * G.2 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4^6 * G.3 * G.4 * G.2 * G.4^-4 * G.1 * G.3 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^11 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-3 * G.2 * G.4^4 * G.1 * G.4 * G.3 * G.2 * G.4^4 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-4 * G.2 * G.3 * G.4^-4 * G.2 * G.4^4 * G.3 * G.4^-4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^2 * G.2 * G.4^6 * G.3 * G.1 * G.4 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-4 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.4^-6 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-7 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.4^4 * G.3 * G.4^-4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^7 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^4, G.4 * G.1 * G.4^7 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^7 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.4^-4 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^4 * G.2 * G.4^-2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.1 * G.4^2 * G.3 * G.4^-3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4^-4 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-5 * G.1 * G.4^2 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.1 * G.4 * G.3 * G.4^-4 * G.2 * G.4^-2, G.4^-9 * G.2 * G.3 * G.4^-5 * G.1 * G.4^-3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, (G.2 * G.4^-4 * G.1 * G.4)^2, G.4^-1 * G.2 * G.4^5 * G.3 * G.2 * G.4^5 * G.3 * G.4^-5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^4 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-3 * G.1 * G.4^5 * G.2 * G.1 * G.4 * G.1^2 * G.4^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-5 * G.1 * G.2 * G.1 * G.4^5 * G.2, G.4^4 * G.3 * G.4^-5 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.4^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-6 * G.2 * G.1 * G.4^5 * G.3, G.4^4 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.2 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^2 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-4 * G.2 * G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2)^6, G.3 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.4^-3 * G.2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4^3 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.1, G.4^2 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^5, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^3 * G.1 * G.4 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.1 * G.2)^2, G.3 * G.4^-4 * G.1 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.1 * G.2)^6, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4^3 * G.3 * G.1 * G.4 * G.1 * G.4^-4 * G.1 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, (G.1 * G.4^2 * G.2)^2, G.4 * G.3 * G.1 * G.4^3 * G.1 * G.4^-1 * G.1 * G.4^3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^5, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 * G.2, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4^-1)^4, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3, (G.1 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^4, (G.2 * G.4^-3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.3)^4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.4^3 * G.2 * G.4^-1 * G.1 * G.4^4, (G.2 * G.4^2 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, (G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 432 via quadrangle group [ 2, 2, 2, 18 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-4 * G.1 * G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^7 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^5 * G.3 * G.4^-1 * G.2 * G.4^6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4^-3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^7 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^2 * G.1 * G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6 * G.3 * G.4^-1 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-3 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^7 * G.3 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-4 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^26, G.4 * G.3 * G.4^-7 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-6 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^26, G.3 * G.4^-9 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^7 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^16 * G.1 * G.4 * G.1^2 * G.3 * G.4^-6 * G.2 * G.4^2 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-14 * G.2 * G.4^5 * G.3 * G.1 * G.4^-6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^15 * G.3 * G.4^-5 * G.2 * G.3 * G.2 * G.4^4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^5 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.4^-13 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2, G.4^-2 * G.1 * G.4^6 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-12 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^8 * G.3 * G.4^-6 * G.1 * G.4 * G.3 * G.1 * G.4^9 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-12 * G.1 * G.4^5 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-8 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 * G.2 * G.4^3 * G.3 * G.4^-8 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-10 * G.1 * G.4 * G.2 * G.1 * G.4^12 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-17 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.4^6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^11 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^13 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4 * G.3 * G.4^-2 * G.2 * G.4^4 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4^19 * G.1 * G.3 * G.4^-6 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^26 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^26 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^19 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^5 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^6 * G.3 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^14 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4^3 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^26 ] Genus 97 action of group of order 416 via quadrangle group [ 2, 2, 2, 26 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-8 * G.3 * G.4^-6 * G.1^2 * G.4^-5 * G.1 * G.4^4 * G.2 * G.4^-2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^7 * G.3 * G.1^2 * G.4^-9 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3)^4, G.2 * G.4^7 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^11 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^7 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-7 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^4 * G.3 * G.1 * G.4^-9 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.4^-6 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-6 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-4 * G.1 * G.4^-1 * G.1 * G.4^-2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-2 * G.1 * G.4^5 * G.1^2 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.4^-13 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^11 * G.3 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-13 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^10 * G.3 * G.4^-1 * G.1 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^2 * G.3 * G.4^-2 * G.1 * G.4^5 * G.1^2 * G.4 * G.2 * G.4^5 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^5 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4^-5 * G.1 * G.4^2 * G.3 * G.4^-2 * G.1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.4^5 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.4^-10 * G.1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4^-9 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-9 * G.3 * G.1 * G.4^4 * G.2 * G.4^-2 * G.1 * G.2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^6 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4^9 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^11 * G.2 * G.1 * G.4^5, G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-6 * G.1 * G.4^2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-9 * G.1 * G.4^7 * G.2 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.3 * G.4 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-34 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^28 * G.1^2 * G.4^6 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4^8 * G.3 * G.4^-6 * G.1^2 * G.4^-1 * G.1 * G.4^-14 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4 * G.3 * G.4^-5 * G.2 * G.4^19 * G.1^2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^5 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^34 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^34 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^10 * G.3 * G.4^-6 * G.2 * G.4^-1 * G.2 * G.1 * G.4^5 * G.2 * G.4^11 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^7 * G.2 * G.4^10 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 * G.4^8 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-25 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12 * G.2 * G.4^-5 * G.1 * G.2 * G.4^-1 * G.1 * G.4^14 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^3 * G.2 * G.4^-13 * G.3 * G.4^-5 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^9 ] Genus 97 action of group of order 408 via quadrangle group [ 2, 2, 2, 34 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^5 * G.2 * G.4^-1 * G.1 * G.4^20 * G.2 * G.4^-1 * G.1 * G.4^5 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-7 * G.2 * G.4^3 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4^6 * G.3 * G.1^2 * G.2 * G.4^18 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^14 * G.3 * G.4^-7 * G.2 * G.4^3 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.4 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^14 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^16 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-20 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^16 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^18 * G.3 * G.4^-1 * G.1 * G.4^5 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^19 * G.2 * G.1 * G.4^5 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.4^-3 * G.3 * G.4^-6 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^-3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4^-18 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-50 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-24 * G.2 * G.4^12 * G.3 * G.2 * G.4 * G.3 * G.4^-11 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^34 * G.1^2 * G.3 * G.1 * G.3 * G.4^-5 * G.1 * G.4^9 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^25 * G.3 * G.4^-8 * G.2 * G.1 * G.4^16 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^24 * G.2 * G.4^-12 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^20 * G.2 * G.4^-12 * G.1 * G.4 * G.2 * G.1 * G.4^15 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.3 * G.4^-21 * G.2 * G.4 * G.3 * G.4^-16 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^7 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^50 ] Genus 97 action of group of order 400 via quadrangle group [ 2, 2, 2, 50 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-28 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^22 * G.3 * G.4^-4 * G.1 * G.2 * G.1 * G.4^6 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.4^7 * G.3 * G.4^-6 * G.1^2 * G.4^-15 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^6, G.4^4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^19 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^6, G.4^-16 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-15 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.2)^2, G.4^25 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^6, G.4^15 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^14 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^24 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^14 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^16 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-19 * G.1 * G.4^6 * G.2 * G.1 * G.3 * G.1^2 * G.2 * G.4^-6 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^4 * G.2 * G.4^-6 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^17 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^7 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^13 ] Genus 97 action of group of order 396 via quadrangle group [ 2, 2, 2, 66 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-5 * G.1 * G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-29 * G.1^2 * G.2 * G.4^19 * G.3 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-28 * G.1^2 * G.2 * G.4^19 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^41 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-43 * G.1 * G.3 * G.4^-5 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-21 * G.1 * G.4^21 * G.2 * G.4^-6 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-21 * G.1 * G.4^20 * G.1 * G.4^-1 * G.1 * G.4^6 * G.2 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-98 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-98 ] Genus 97 action of group of order 392 via quadrangle group [ 2, 2, 2, 98 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^77 * G.2 * G.1 * G.2 * G.1 * G.4^19 ] Genus 97 action of group of order 388 via quadrangle group [ 2, 2, 2, 194 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-48 * G.2 * G.3 * G.4^-48 ] Genus 97 action of group of order 388 via quadrangle group [ 2, 2, 2, 194 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-89 * G.1 * G.3 * G.4^-7 ] Genus 97 action of group of order 388 via quadrangle group [ 2, 2, 2, 194 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^77 * G.1^2 * G.2 * G.1 * G.4^19 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-2 * G.1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1)^2, G.2 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3 * G.1 * G.3^-1 * G.1)^6, G.2 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^12, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-2 * G.2 * G.3^-1 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.4 * G.3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3 * G.1 * G.3^-1)^3, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2)^4, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.2)^4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4, (G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4, G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3^-1 * G.4^-1, (G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.3 * G.4^-1 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.3^-1 * G.4 * G.3^-1)^2, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.4 * G.3^-1 * G.1 * G.4)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3^-1, G.3^-1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, G.3^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.3 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3^-1 * G.4^-1)^2, G.4 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, (G.1 * G.3^-1)^4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1)^4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3^-1)^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.2 * G.4 * G.3^-1 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3^-1 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.4 * G.3)^2, (G.1 * G.3^-1)^4, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3^-1 * G.4^-1 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.3^-1 * G.4^-1 * G.2)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3^-1 * G.4^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.3 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.4 * G.3^-1 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.1 * G.3^-1 * G.1 * G.2)^2, (G.1 * G.2 * G.4^-1 * G.2)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, (G.1 * G.3^-1)^4, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.3 * G.4^-1, (G.2 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.2^-1 * G.3)^3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, (G.2^-1 * G.4^-1)^4, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.3 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2^-1 * G.3 * G.2 * G.3 * G.1)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.3)^6, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2^2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.4 * G.3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.3 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, (G.2 * G.1)^6 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.4^-1)^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.4^-1)^4, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4^-1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.4, (G.2 * G.4^-1)^6, G.3 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1 * G.4^-1)^6, G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.2^-1, G.4^-1)^2, G.3 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4, (G.2^-1, G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4, (G.2^-1, G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, (G.2^-1, G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.4 * G.3 * G.2, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.4^-1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, G.2^-1 * G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1 * G.4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1, (G.2 * G.3 * G.2^-1 * G.3)^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 * G.2^-1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.3 * G.2 * G.1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2^-1 * G.3)^4, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1, G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1)^4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4, (G.2^-1, G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.4^-1 * G.2^-1)^3, (G.1 * G.3 * G.2^-1 * G.3)^2, (G.2^-1 * G.4 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1)^4, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2 * G.4^-1 * G.2^-1 * G.3)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.3 * G.1 * G.2^-1 * G.4 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2^-1 * G.4^-1 * G.2 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.1 * G.4 * G.2^-1, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.3 * G.1)^3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.2^-1 * G.1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2^-1)^3, G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2^-1 * G.1)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1)^2, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.1)^4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3, (G.2^-1, G.4^-1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2^-1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4 * G.2^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1)^4, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2)^3, (G.2^-1 * G.1)^4, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.2^-1 * G.3)^4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.2 * G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.2^-1 * G.1)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, (G.2^-1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2, G.4), G.4^-3, G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^-2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2^-1, G.1 * G.3 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 97 action of group of order 576 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2^-1 * G.3)^4 ] Largest orientation-preserving group for genus 97 has order 3840 ... group action with signature (0: +; [2,4,5]; {-}) Largest group with or without reflections for genus 97 has order 7680 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest group with reflections for genus 97 has order 7680 ... group action with signature (0; +; [-]; {(2,4,5)}) Largest chiral group for genus 97 has order 3840 ... group action with signature (0: +; [2,4,5]; {-}) Largest non-orientable group for non-orientable genus 98 has order 1920 ... group action with signature (0; +; [-]; {(2,5,5)}) Check total 8003 : 4336 chiral, 3667 reflexible, with 507 non-orientable quotient actions Genus 98 actions: Genus 98 action of group of order 792 via triangle group [ 2, 4, 198 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-198 ] Genus 98 action of group of order 784 via triangle group [ 2, 4, 392 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-50 * G.1 * G.2^-1 * G.3^-145 ] Genus 98 action of group of order 1164 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 98 action of group of order 1164 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 ] Genus 98 action of group of order 1164 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 ] Genus 98 action of group of order 1164 via triangle group [ 2, 6, 6 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2^2 ] Genus 98 action of group of order 600 via triangle group [ 2, 6, 100 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^-62 * G.1 * G.3^17 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-17 ] Genus 98 action of group of order 588 via triangle group [ 2, 6, 294 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^-59 * G.1 * G.3^13 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-6 * G.1 * G.3 * G.2^-1 * G.3^-8 ] Genus 98 action of group of order 776 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-3 * G.1 ] Genus 98 action of group of order 776 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3 * G.2 * G.3^-1 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 98 action of group of order 776 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 98 action of group of order 776 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 98 action of group of order 528 via triangle group [ 2, 8, 132 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^-41 * G.1 * G.3^5 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-11 ] Genus 98 action of group of order 490 via triangle group [ 2, 10, 245 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^10, G.3^33 * G.2 * G.3^-8 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^2 ] Genus 98 action of group of order 480 via triangle group [ 2, 12, 80 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^-7 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3^4 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-16 ] Genus 98 action of group of order 480 via triangle group [ 2, 16, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-4 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2, G.3^17 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3^4 ] Genus 98 action of group of order 440 via triangle group [ 2, 20, 110 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-8 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^11 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-1 * G.1 ] Genus 98 action of group of order 448 via triangle group [ 2, 28, 32 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^5 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 98 action of group of order 420 via triangle group [ 2, 30, 210 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-17 * G.3^4 * G.2^-5 * G.3^4 ] Genus 98 action of group of order 420 via triangle group [ 2, 42, 70 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2^2 ] Genus 98 action of group of order 406 via triangle group [ 2, 58, 203 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2, G.2^-16 * G.3^4 * G.2^-6 * G.3^3 ] Genus 98 action of group of order 408 via triangle group [ 2, 68, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^2 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-1 * G.1, G.2^-21 * G.3^4 * G.2^-6 * G.3^2 * G.2^-1 ] Genus 98 action of group of order 400 via triangle group [ 2, 100, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-13 * G.2^12 * G.3^-4 * G.2^18 * G.3^-3 ] Genus 98 action of group of order 394 via triangle group [ 2, 197, 394 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^131 * G.2^-64 * G.3 ] Genus 98 action of group of order 396 via triangle group [ 2, 198, 198 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^66 * G.3^-132 ] Genus 98 action of group of order 392 via triangle group [ 2, 392, 392 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^65 * G.3^-131 ] Genus 98 action of group of order 582 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 98 action of group of order 582 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 98 action of group of order 582 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 98 action of group of order 582 via triangle group [ 3, 6, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 98 action of group of order 396 via triangle group [ 4, 4, 99 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^83 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 98 action of group of order 392 via triangle group [ 4, 4, 196 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^82 * G.2 * G.1^-1 * G.3^15 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^5 * G.1 * G.3 * G.2 * G.4^5 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^5 * G.3 * G.1 * G.2 * G.4^5 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4^5 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.2 * G.1 * G.4^6 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.2 * G.4 * G.2 * G.4^4 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-49 * G.2 * G.1 * G.3 * G.4^-49 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^99 ] Genus 98 action of group of order 396 via quadrangle group [ 2, 2, 2, 99 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-77 * G.1 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 98 action of group of order 392 via quadrangle group [ 2, 2, 2, 196 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-49 * G.1 * G.4^-49 ] Genus 98 action of group of order 392 via quadrangle group [ 2, 2, 2, 196 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-8 * G.1 * G.3 * G.4^-89 ] Genus 98 action of group of order 392 via quadrangle group [ 2, 2, 2, 196 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^77 * G.2 * G.1 * G.4^20 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.1^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.3^-1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.2 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.1^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.4 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.2 * G.4^-1 * G.3^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.4 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.3^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2^2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2^2 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.3 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.3 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, G.1 * G.3 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.3 * G.2^-1 * G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.2^-1 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 98 action of group of order 582 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Largest orientation-preserving group for genus 98 has order 1164 ... group action with signature (0: +; [2,6,6]; {-}) Largest group with or without reflections for genus 98 has order 1584 ... group action with signature (0; +; [-]; {(2,4,198)}) Largest group with reflections for genus 98 has order 1584 ... group action with signature (0; +; [-]; {(2,4,198)}) Largest chiral group for genus 98 has order 1164 ... group action with signature (0: +; [2,6,6]; {-}) Largest non-orientable group for non-orientable genus 99 has order 582 ... group action with signature (0; +; [2,3]; {(1)}) Check total 436 : 396 chiral, 40 reflexible, with 8 non-orientable quotient actions Genus 99 actions: Genus 99 action of group of order 2352 via triangle group [ 2, 3, 12 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 99 action of group of order 2352 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 ] Genus 99 action of group of order 2352 via triangle group [ 2, 3, 12 ] Action is chiral [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 * G.1, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 2058 via triangle group [ 2, 3, 14 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^7 * G.2 * G.3^-1 * G.1^2 * G.2^-1 * G.3^-1 * G.1 * G.3^6 ] Genus 99 action of group of order 1568 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 99 action of group of order 1568 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 ] Genus 99 action of group of order 1176 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 99 action of group of order 816 via triangle group [ 2, 4, 102 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^2, G.3^-83 * G.1 * G.3^10 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-6 ] Genus 99 action of group of order 800 via triangle group [ 2, 4, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-82 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-7 ] Genus 99 action of group of order 800 via triangle group [ 2, 4, 200 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-200 ] Genus 99 action of group of order 792 via triangle group [ 2, 4, 396 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-51 * G.1 * G.2^-1 * G.3^-146 ] Genus 99 action of group of order 624 via triangle group [ 2, 6, 52 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-8 * G.1 * G.3^6 * G.2 * G.1 * G.2 * G.3^-7 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 686 via triangle group [ 2, 7, 14 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 2, 8, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^3, G.1 * G.3 * G.2^3 * G.1 * G.3 * G.2 * G.1 * G.2^-3 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 99 action of group of order 784 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2^2 * G.3^-1 * G.1 * G.3 ] Genus 99 action of group of order 672 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, (G.2^3 * G.3^-1)^3 ] Genus 99 action of group of order 672 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, G.3^3 * G.2^-3 * G.3^-1 * G.2 * G.1 * G.2^-2 ] Genus 99 action of group of order 672 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 99 action of group of order 672 via triangle group [ 2, 8, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-4, G.3^2 * G.2^-4 * G.3^-2 * G.2 * G.1 * G.2^-1 ] Genus 99 action of group of order 544 via triangle group [ 2, 8, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-31 * G.1 * G.3^20 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 99 action of group of order 544 via triangle group [ 2, 8, 68 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^45 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^15 ] Genus 99 action of group of order 528 via triangle group [ 2, 8, 264 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-28 * G.1 * G.3^21 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 99 action of group of order 528 via triangle group [ 2, 8, 264 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-28 * G.1 * G.3^21 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 99 action of group of order 588 via triangle group [ 2, 12, 12 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.3^3 ] Genus 99 action of group of order 588 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 ] Genus 99 action of group of order 588 via triangle group [ 2, 12, 12 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.3^3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 99 action of group of order 480 via triangle group [ 2, 12, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^12, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 99 action of group of order 480 via triangle group [ 2, 12, 120 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-4 * G.1 * G.3^22 * G.2^-1 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 99 action of group of order 490 via triangle group [ 2, 14, 35 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-4 * G.2^5 * G.3^-4, G.3^-3 * G.1 * G.3^8 * G.2 * G.1 * G.3^5 * G.2^-1 * G.3^-17 ] Genus 99 action of group of order 462 via triangle group [ 2, 14, 231 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2 * G.3^-4 * G.2^5 * G.3^-4, G.3^-2 * G.1 * G.3^8 * G.2 * G.1 * G.3^4 * G.2^-1 * G.3^-17 ] Genus 99 action of group of order 480 via triangle group [ 2, 15, 40 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^4 * G.2^2 * G.1 * G.3^3 ] Genus 99 action of group of order 480 via triangle group [ 2, 20, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, (G.2 * G.3^-1 * G.2^2)^2, G.3^6 * G.2 * G.3^-5 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^8 * G.1 * G.3 * G.2^6 ] Genus 99 action of group of order 480 via triangle group [ 2, 20, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-4 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-6, G.3^14 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 * G.1 * G.3 ] Genus 99 action of group of order 440 via triangle group [ 2, 20, 220 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-8 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^9 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-5 ] Genus 99 action of group of order 432 via triangle group [ 2, 27, 108 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3 * G.2^-7 * G.3^3 * G.2^-12 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 99 action of group of order 418 via triangle group [ 2, 38, 209 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3 * G.2^-6 * G.3^4 * G.2^-2 * G.3^6 ] Genus 99 action of group of order 414 via triangle group [ 2, 46, 207 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^6 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-4, G.2^-10 * G.3^4 * G.2^-4 * G.3^5 ] Genus 99 action of group of order 416 via triangle group [ 2, 52, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2 * G.3^-18 * G.2^10 * G.3^-5 * G.2 * G.3^-15 * G.2^2 ] Genus 99 action of group of order 416 via triangle group [ 2, 52, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.3^-13 * G.2^12 * G.3^-4 * G.2^21 * G.3^-1 ] Genus 99 action of group of order 408 via triangle group [ 2, 68, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-31 * G.2^13 * G.3^-2 * G.2^21 * G.3^-1 ] Genus 99 action of group of order 408 via triangle group [ 2, 102, 102 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-2, G.2^-1 * G.3 * G.2^-97 * G.3 * G.2^-1 * G.3 ] Genus 99 action of group of order 402 via triangle group [ 2, 134, 201 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2 * G.3^-30 * G.2^13 * G.3^-2 * G.2^20 * G.3^-1 ] Genus 99 action of group of order 398 via triangle group [ 2, 199, 398 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^132 * G.2^-66 ] Genus 99 action of group of order 400 via triangle group [ 2, 200, 200 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^67 * G.3^-132 * G.2 ] Genus 99 action of group of order 400 via triangle group [ 2, 200, 200 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-64 * G.2^33 * G.3^-2 ] Genus 99 action of group of order 396 via triangle group [ 2, 396, 396 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^66 * G.3^-131 * G.2 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-2 * G.1^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.2^-1 * G.3^-2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3 * G.2 * G.1 * G.3)^3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^2 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.1, G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3 * G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, G.3 * G.1^-1 * G.3^2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 * G.1 * G.3, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, (G.3 * G.2 * G.1 * G.3)^3, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, (G.2 * G.1^-1 * G.3)^3, (G.3 * G.2 * G.1 * G.3)^3, G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1, G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 99 action of group of order 1176 via triangle group [ 3, 3, 6 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^6, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1, G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 ] Genus 99 action of group of order 1029 via triangle group [ 3, 3, 7 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^3 * G.2^-1 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 ] Genus 99 action of group of order 624 via triangle group [ 3, 3, 52 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^5 * G.2^-1 * G.3^-3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^5 ] Genus 99 action of group of order 624 via triangle group [ 3, 3, 52 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2^-1 * G.3^-7 ] Genus 99 action of group of order 597 via triangle group [ 3, 3, 199 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^10 * G.2 * G.3^-1 * G.1 * G.3^3 ] Genus 99 action of group of order 597 via triangle group [ 3, 3, 199 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-7 ] Genus 99 action of group of order 672 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 672 via triangle group [ 3, 4, 8 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^8, G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 99 action of group of order 588 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.1^-1 * G.3)^3, G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 99 action of group of order 588 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.2 * G.1^-1 * G.3)^3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 99 action of group of order 588 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 588 via triangle group [ 3, 4, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 ] Genus 99 action of group of order 588 via triangle group [ 3, 4, 12 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3 * G.2^-1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^2 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.1^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-2 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.2 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.3 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 ] Genus 99 action of group of order 784 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.3 * G.1^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2^-1 * G.3^-2 * G.1^2 * G.3^2 * G.2^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.3^-1 * G.1 * G.3^-1 * G.2 * G.1 * G.3^-2 * G.2 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1 * G.3^-2 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 ] Genus 99 action of group of order 588 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2^-1 * G.1)^3, G.3^6, G.2 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^3 ] Genus 99 action of group of order 408 via triangle group [ 4, 4, 51 ] Action is reflexible [m,n] and there is a non-orientable quotient [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, (G.2 * G.3^-1)^2, G.3^-40 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-7 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.3 * G.1^-1 * G.3^4 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^4 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-39 * G.1 * G.3 * G.2 * G.3^-9 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-39 * G.1 * G.2^-1 * G.3^-10 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-4 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^84 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 ] Genus 99 action of group of order 400 via triangle group [ 4, 4, 100 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-38 * G.1^-1 * G.3^2 * G.2 * G.3^-9 ] Genus 99 action of group of order 396 via triangle group [ 4, 4, 198 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^83 * G.2^-1 * G.1 * G.3^15 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.4^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 * G.2 * G.3 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-2 * G.1 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 784 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4^6, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-2)^2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-2 * G.1 * G.3 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4^2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.1 * G.4 * G.1^2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 588 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4^-9, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.3 * G.4^-3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-9, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-9, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.1 * G.4)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-9, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.3 * G.1)^3, G.2 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-9, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1 * G.4)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-9, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1 * G.4)^3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-9, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.1 * G.4^4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-9, G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-9, G.4^2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-2 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.4^-1 * G.2 * G.4^-1)^3 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1, G.4^4 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-3 * G.1 * G.4^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-9, G.4^-1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.3 * G.1 * G.4)^3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.4^4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2, G.4^2 * G.2 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1, G.4^2 * G.2 * G.4^-1 * G.1 * G.4^-3 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4^-1, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^4, (G.4^-1 * G.2 * G.4^-1)^3, G.2 * G.4^-3 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, (G.4^-1 * G.2 * G.4^-1)^3, G.2 * G.4^3 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-9, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.2 * G.1)^3, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-9 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^3, G.4^-9, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-3 * G.1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^2 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-3 * G.1 * G.4^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.2 * G.4 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-2 * G.2 * G.3 * G.1 * G.4^-2 * G.2 * G.4^-1 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.2 ] Genus 99 action of group of order 504 via quadrangle group [ 2, 2, 2, 9 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^2 * G.3 * G.4^-1 * G.1 * G.4^2 * G.3 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.4^-16 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.1 * G.4^4 * G.3 * G.4^-4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.3 * G.4^-4 * G.2 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^6 * G.3 * G.1^2 * G.4^-5 * G.2 * G.3 * G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10 * G.3 * G.2 * G.1 * G.4^5, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^3 * G.3 * G.4^-5 * G.1 * G.2 * G.4^7, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-4 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-9 * G.1 * G.3 * G.1 * G.3 * G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^9 * G.3 * G.4^-1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^6 * G.3 * G.4^-1 * G.1 * G.4^7 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-4 * G.1 * G.4^3 * G.3 * G.4^-1 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.1^2 * G.4^-8, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^3 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-3 * G.1 * G.4^7 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.4^8 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^-5 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^6 * G.3 * G.1^2 * G.4^-5 * G.2 * G.3 * G.4^-3, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-5 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10 * G.3 * G.2 * G.1 * G.4^5, G.1 * G.3 * G.4^-6 * G.2 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.1 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4^5 * G.3 * G.1 * G.3 * G.1^2 * G.4^-8, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-3 * G.1 * G.4^7 * G.1^2 * G.2 * G.1 * G.2 * G.4^-4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^3 * G.3 * G.4^-5 * G.1 * G.2 * G.4^7, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^3 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.4^6, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-6 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.4^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^-10 * G.1 * G.3 * G.1^2 * G.4^-1 * G.1 * G.3 * G.4^-3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-9 * G.1 * G.3 * G.1 * G.3 * G.4^-5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.4^4, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-5 * G.1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 99 action of group of order 448 via quadrangle group [ 2, 2, 2, 16 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-5 * G.1 * G.4 * G.1^2 * G.4 * G.2 * G.4^-5 * G.1 * G.4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^4 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-7 * G.2 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.3 * G.4^-5 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^8 * G.1^2 * G.4 * G.3 * G.4^-5 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-7 * G.2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^6 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^9 * G.1 * G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.3 * G.4^-5 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3, G.4^-5 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-4 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.3 * G.4^-8 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 * G.1 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^8 * G.3 * G.4^-1 * G.1 * G.4^5, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-6 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^3 * G.3 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4^5 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-5 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^9 * G.3 * G.1 * G.4^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^5 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-4 * G.1 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^6 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^7 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.3 * G.4 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4^4 * G.3 * G.4^5 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^4 * G.2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.4 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.4^7 * G.1^2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^4 * G.3 * G.4^2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-4 * G.1 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 99 action of group of order 420 via quadrangle group [ 2, 2, 2, 30 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^8 * G.2 * G.1 * G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-25 * G.2 * G.1 * G.3 * G.4^-25 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.4 * G.2, G.4^-45 * G.1^2 * G.4^-6 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.3 * G.1, G.4^37 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.2 * G.4^6 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1,2] and there is a non-orientable quotient [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.2, G.4^51 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^51 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-43 * G.1^2 * G.4^-8 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.4^-1, G.4^-37 * G.1 * G.4 * G.2 * G.4^-3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4^-2, G.4^38 * G.2 * G.3 * G.4^-3 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 99 action of group of order 408 via quadrangle group [ 2, 2, 2, 51 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^51 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-100 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-91 * G.1^2 * G.4^-9 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^91 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-20 * G.2 * G.4 * G.3 * G.4^-16 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.4^7 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-44 * G.2 * G.1 * G.3 * G.4^-5 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^-27 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-20 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-25 * G.1 * G.4^-1 * G.1 * G.4^-24 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-23 * G.2 * G.4^13 * G.3 * G.1 * G.4^-13 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^34 * G.1^2 * G.3 * G.1 * G.3 * G.4^-4 * G.1 * G.4^10 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^23 * G.2 * G.4^-12 * G.1 * G.2 * G.1 * G.4^13 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^25 * G.3 * G.4^-8 * G.2 * G.1 * G.2 * G.4^5 * G.2 * G.4^11 ] Genus 99 action of group of order 400 via quadrangle group [ 2, 2, 2, 100 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^20 * G.2 * G.4^-12 * G.1 * G.2 * G.4^-4 * G.1 * G.4^12 ] Genus 99 action of group of order 396 via quadrangle group [ 2, 2, 2, 198 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-49 * G.2 * G.3 * G.4^-49 ] Genus 99 action of group of order 396 via quadrangle group [ 2, 2, 2, 198 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^91 * G.2 * G.4^8 ] Genus 99 action of group of order 396 via quadrangle group [ 2, 2, 2, 198 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-78 * G.1 * G.2 * G.4^-20 ] Largest orientation-preserving group for genus 99 has order 2352 ... group action with signature (0: +; [2,3,12]; {-}) Largest group with or without reflections for genus 99 has order 4704 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest group with reflections for genus 99 has order 4704 ... group action with signature (0; +; [-]; {(2,3,12)}) Largest chiral group for genus 99 has order 2352 ... group action with signature (0: +; [2,3,12]; {-}) Largest non-orientable group for non-orientable genus 100 has order 816 ... group action with signature (0; +; [-]; {(2,4,102)}) Check total 773 : 580 chiral, 193 reflexible, with 57 non-orientable quotient actions Genus 100 actions: Genus 100 action of group of order 1296 via triangle group [ 2, 3, 72 ] Action is reflexible [m] [ G.1^2, G.2^-3, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2 * G.3^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-7 ] Genus 100 action of group of order 1320 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^3, G.3^10, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 100 action of group of order 1320 via triangle group [ 2, 4, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, (G.3^-1 * G.2)^5, G.3^10 ] Genus 100 action of group of order 1080 via triangle group [ 2, 4, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.3^-1 * G.2)^5, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^3 * G.2^-1 * G.3^2 ] Genus 100 action of group of order 968 via triangle group [ 2, 4, 22 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^-22 ] Genus 100 action of group of order 808 via triangle group [ 2, 4, 202 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-202 ] Genus 100 action of group of order 800 via triangle group [ 2, 4, 400 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-52 * G.1 * G.2^-1 * G.3^-147 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.3^-21 * G.1 * G.3^8 * G.2 * G.3^-6 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, (G.2 * G.3^-1 * G.2 * G.3^-1 * G.2)^2, G.3^2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-20 * G.1 * G.3^9 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3^4 * G.2 * G.3^-3 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-3 * G.3^-2 * G.2^2, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-4 * G.1 * G.3^5 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-12 * G.1 * G.3^11 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-4 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1, G.3^-19 * G.1 * G.3^3 * G.2 * G.3^-7 * G.1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 2, 6, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^6, G.1 * G.3 * G.2 * G.3^-3 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 100 action of group of order 612 via triangle group [ 2, 6, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-20 * G.1 * G.3^7 * G.2^-1 * G.3^-6 ] Genus 100 action of group of order 612 via triangle group [ 2, 6, 102 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^6, G.3^82 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.3^-6 * G.1 * G.3^11 ] Genus 100 action of group of order 612 via triangle group [ 2, 6, 102 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^76 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 100 action of group of order 600 via triangle group [ 2, 6, 300 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^59 * G.2 * G.1 * G.3^14 * G.2 * G.3^-1 * G.1 * G.3^7 * G.2 * G.3^-7 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^3 ] Genus 100 action of group of order 672 via triangle group [ 2, 7, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, (G.3 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 100 action of group of order 672 via triangle group [ 2, 7, 16 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-7, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^-1 * G.2 * G.1 * G.2^-3 * G.3^-1 * G.2 * G.3^-3 ] Genus 100 action of group of order 720 via triangle group [ 2, 8, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.3^-1 * G.2)^3, G.2^8, (G.2 * G.3^-2 * G.2^2)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1 ] Genus 100 action of group of order 720 via triangle group [ 2, 8, 10 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, (G.3^-1 * G.2)^5 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2^-9, (G.2 * G.3^-2 * G.2 * G.3^-1)^2 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^4, G.2^-9, (G.3 * G.2^-1 * G.3)^3 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^12 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^12 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^12 ] Genus 100 action of group of order 648 via triangle group [ 2, 9, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1 * G.2)^2, G.2^-9, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.3^12 ] Genus 100 action of group of order 540 via triangle group [ 2, 9, 45 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^-9, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.1 * G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2 * G.3^-2 * G.2 * G.3^-2 ] Genus 100 action of group of order 520 via triangle group [ 2, 10, 52 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^10, G.3^28 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2 * G.3^-8 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^8 ] Genus 100 action of group of order 504 via triangle group [ 2, 12, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-1 * G.1 * G.3^25 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-9 ] Genus 100 action of group of order 504 via triangle group [ 2, 12, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^12, (G.2 * G.3^-1 * G.2^4)^2, G.3^-7 * G.1 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 100 action of group of order 504 via triangle group [ 2, 12, 42 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^12, G.3^15 * G.2 * G.1 * G.3^3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-9 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.3^7 ] Genus 100 action of group of order 480 via triangle group [ 2, 12, 240 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^12, G.3^-1 * G.1 * G.3^24 * G.2 * G.3^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-8 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-5 * G.3^5 * G.2^-3 * G.3^5, G.3^-1 * G.1 * G.3^13 * G.2 * G.3^-5 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-2 * G.1 * G.3 * G.2^3 * G.3^-5 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-5 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3 * G.2^-2 * G.3 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-1 * G.3 * G.2^-3 * G.3^4 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-4, G.3^3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2^-4 * G.3^2 * G.2^-2 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^3 * G.2^-1 ] Genus 100 action of group of order 486 via triangle group [ 2, 18, 27 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.3^2 * G.2^-3 * G.3 * G.2^-1 * G.3^2 ] Genus 100 action of group of order 450 via triangle group [ 2, 18, 225 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-6 * G.3^4 * G.2^-3 * G.3^4 * G.2^-1, G.3^-1 * G.1 * G.3^12 * G.2 * G.3^-4 * G.1 * G.3^4 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 484 via triangle group [ 2, 22, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^-9 * G.3^5 * G.2^-3 * G.3^5, G.3^-1 * G.1 * G.3^9 * G.2 * G.3^-5 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 100 action of group of order 484 via triangle group [ 2, 22, 22 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.2^-1 * G.3^4 * G.2^-1 * G.3^4 * G.2^-4 * G.3 * G.2^-6 * G.3, G.2^2 * G.1 * G.2^-3 * G.3^-1 * G.2^2 * G.1 * G.2^-5 * G.3 * G.2^5 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 100 action of group of order 484 via triangle group [ 2, 22, 22 ] Action is reflexible [m,n] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^-5 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-7, G.3^11 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^3 ] Genus 100 action of group of order 440 via triangle group [ 2, 22, 220 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^8 * G.2 * G.3^-4 * G.1 * G.3 * G.2^-1 * G.3^-5, G.2^-9 * G.3^4 * G.2^-5 * G.3^4 ] Genus 100 action of group of order 432 via triangle group [ 2, 36, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.3^3 * G.2^-2 * G.3^4 * G.2^-4 * G.3^5 ] Genus 100 action of group of order 432 via triangle group [ 2, 36, 72 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.2^-6 * G.3^-1 * G.2^5, G.3^2 * G.2^-1 * G.3 * G.2^-4 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^2 * G.2^-2 * G.3 ] Genus 100 action of group of order 420 via triangle group [ 2, 42, 210 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.3^-5 * G.2^10 * G.3^-4 * G.2^22 * G.3^-1 ] Genus 100 action of group of order 416 via triangle group [ 2, 52, 208 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2 * G.3^-4 * G.1 * G.3^3 * G.2^-1 * G.3^-3, G.2^-13 * G.3^4 * G.2^-4 * G.3^4 * G.2^-1 ] Genus 100 action of group of order 414 via triangle group [ 2, 69, 138 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-1 * G.3^-2, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2 * G.3^-33 * G.2^2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-4 * G.2 * G.3^-14 * G.2^2 * G.3^-1 ] Genus 100 action of group of order 410 via triangle group [ 2, 82, 205 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3^4 * G.2^-1 * G.3^-5, G.2 * G.3^-1 * G.2^12 * G.3^-4 * G.2^23 ] Genus 100 action of group of order 408 via triangle group [ 2, 102, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-65 * G.2^35 * G.3^-1 ] Genus 100 action of group of order 402 via triangle group [ 2, 201, 402 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^133 * G.2^-66 * G.3 ] Genus 100 action of group of order 404 via triangle group [ 2, 202, 202 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^68 * G.3^-134 ] Genus 100 action of group of order 400 via triangle group [ 2, 400, 400 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^67 * G.3^-133 ] Genus 100 action of group of order 648 via triangle group [ 3, 3, 36 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^2 ] Genus 100 action of group of order 648 via triangle group [ 3, 3, 36 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-4 * G.1^-1 * G.3 * G.2^-1 * G.1^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 648 via triangle group [ 3, 3, 36 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 100 action of group of order 603 via triangle group [ 3, 3, 201 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1^-1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 ] Genus 100 action of group of order 603 via triangle group [ 3, 3, 201 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.3^-3 * G.1 * G.3^5 * G.2 * G.3^-7 ] Genus 100 action of group of order 648 via triangle group [ 3, 4, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^4 * G.2^-1 * G.1^-1 * G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 100 action of group of order 648 via triangle group [ 3, 4, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1 * G.2^-1, G.2^-1 * G.3^2 * G.2^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 100 action of group of order 648 via triangle group [ 3, 4, 9 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^2, G.2^-1 * G.3^2 * G.2^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 100 action of group of order 660 via triangle group [ 3, 5, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.3^6, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^2, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 100 action of group of order 660 via triangle group [ 3, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1, G.2^-5, G.3^6, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 100 action of group of order 660 via triangle group [ 3, 5, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1^-1 * G.2^2 * G.1^-1 * G.2^2 * G.1 * G.3^-1 ] Genus 100 action of group of order 660 via triangle group [ 3, 5, 6 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-5, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3^2, (G.3^-1 * G.2)^3, G.1^-1 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.3^-1 ] Genus 100 action of group of order 432 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3^-1 * G.2 * G.1^-1 * G.2^-2, G.2^6, G.3^-4 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 100 action of group of order 432 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.1^-1 * G.3^2 * G.2^-1 * G.1 * G.3^3 ] Genus 100 action of group of order 432 via triangle group [ 3, 6, 24 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^6, (G.3^-1 * G.2)^3, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, (G.1 * G.3 * G.2^-1 * G.3^-1)^2 ] Genus 100 action of group of order 402 via triangle group [ 3, 6, 134 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-4 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-3 ] Genus 100 action of group of order 402 via triangle group [ 3, 6, 134 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2 * G.3^-2 * G.2 * G.1^-1 * G.3^5 ] Genus 100 action of group of order 432 via triangle group [ 3, 8, 12 ] Action is reflexible [m] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.2^2 * G.1^-1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.2 * G.1^-1 * G.3 * G.2^-2, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 484 via triangle group [ 4, 4, 11 ] Action is reflexible [m,n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6 * G.2^-1 * G.1^3 * G.3^4 ] Genus 100 action of group of order 404 via triangle group [ 4, 4, 101 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^6 * G.2 * G.1 * G.3^4 ] Genus 100 action of group of order 404 via triangle group [ 4, 4, 101 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^85 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 100 action of group of order 404 via triangle group [ 4, 4, 101 ] Action is reflexible [n] and there is a non-orientable quotient [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3^-5 * G.2 * G.1 * G.3^-5 ] Genus 100 action of group of order 400 via triangle group [ 4, 4, 200 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^84 * G.2^-1 * G.1 * G.3^15 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.2^2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.2 * G.1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3, G.3^8, G.2 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.3^3 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8, G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.1^-1 * G.3 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.3 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, (G.2 * G.3^-2)^2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.3^-2 * G.2 * G.1^2 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.1^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^2 * G.2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-2 * G.1^-1 * G.2 * G.3^-1, G.2^6, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.2^2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^3 * G.2^-1 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, G.3^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.3^-1, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1, G.2^6, (G.2 * G.3^-2)^2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1, G.2^6, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.2^6, G.3^8, G.3^-1 * G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.3^-2 * G.1 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2, G.2^6, G.2^2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 100 action of group of order 432 via triangle group [ 4, 6, 8 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2, G.2^6, G.3 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^4, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1, G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1^2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.2 * G.1 * G.3)^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, (G.1 * G.2 * G.1 * G.3)^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 100 action of group of order 792 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-5, (G.3 * G.1)^5, G.3 * G.4^-2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-5, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-5, (G.3 * G.1)^5, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4^-5, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4 * G.3 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3)^6, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.2 * G.1)^5, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.2 * G.1)^5, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.4^-1 * G.2)^3, G.4^-5, (G.2 * G.1)^5, G.4^2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, (G.2 * G.1)^5, G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-5, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-5, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.4^-1 * G.2)^5, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.3 * G.1)^5 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-5, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-5, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-5, (G.3 * G.1)^5, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-5, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4^-5, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-5, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 100 action of group of order 660 via quadrangle group [ 2, 2, 2, 5 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-5, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 594 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4^2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^8, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4^8, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^8, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^2 * G.3 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^2 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^2 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.4^-2)^2, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^8, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3)^3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.4^8, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^8, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^8, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 ] Genus 100 action of group of order 528 via quadrangle group [ 2, 2, 2, 8 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 ] Genus 100 action of group of order 484 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-11 ] Genus 100 action of group of order 484 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-11 ] Genus 100 action of group of order 484 via quadrangle group [ 2, 2, 2, 11 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^6 * G.1^2 * G.4^5 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.4 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-4 * G.2 * G.1 * G.4^3 * G.3 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 100 action of group of order 432 via quadrangle group [ 2, 2, 2, 24 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 ] Genus 100 action of group of order 404 via quadrangle group [ 2, 2, 2, 101 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-50 * G.2 * G.1 * G.3 * G.4^-50 ] Genus 100 action of group of order 404 via quadrangle group [ 2, 2, 2, 101 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^91 * G.3 * G.1 * G.2 * G.4^9 ] Genus 100 action of group of order 404 via quadrangle group [ 2, 2, 2, 101 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^92 * G.2 * G.1 * G.2 * G.1 * G.4^7 ] Genus 100 action of group of order 400 via quadrangle group [ 2, 2, 2, 200 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-50 * G.1 * G.4^-50 ] Genus 100 action of group of order 400 via quadrangle group [ 2, 2, 2, 200 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-91 * G.1 * G.3 * G.4^-8 ] Genus 100 action of group of order 400 via quadrangle group [ 2, 2, 2, 200 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^92 * G.2 * G.1 * G.4^7 ] Largest orientation-preserving group for genus 100 has order 1320 ... group action with signature (0: +; [2,4,10]; {-}) Largest group with or without reflections for genus 100 has order 2640 ... group action with signature (0; +; [-]; {(2,4,10)}) Largest group with reflections for genus 100 has order 2640 ... group action with signature (0; +; [-]; {(2,4,10)}) Largest chiral group for genus 100 has order 792 ... group action with signature (0; +; [2,2,2,4]; {-}) Largest non-orientable group for non-orientable genus 101 has order 1320 ... group action with signature (0; +; [-]; {(2,4,10)}) Check total 555 : 422 chiral, 133 reflexible, with 30 non-orientable quotient actions Genus 101 actions: Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.3^-1 * G.2)^5, G.3^2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^2 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.1 * G.3^2, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.2^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^8, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, (G.3^-1 * G.2)^5, G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^8, G.3^2 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.3^3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1600 via triangle group [ 2, 4, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.3^8, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^2 * G.3^-2 * G.2 * G.3^-3 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.3^12, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.1 * G.3^2 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-2)^4, G.3^12, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 * G.2, G.2^-1 * G.3 * G.2 * G.1 * G.3^3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^2 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^12, G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3 * G.2 * G.3^-1)^2, G.3^12, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 101 action of group of order 1200 via triangle group [ 2, 4, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3 * G.2 * G.3^-1)^2, G.3^12, G.3^2 * G.2 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.1 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3, (G.2 * G.3^-2)^4 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 1000 via triangle group [ 2, 4, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2, (G.2 * G.3^-2)^4 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^6, (G.2 * G.3^-3 * G.2 * G.3^-1)^2, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^3 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 * G.2, G.1 * G.3^3 * G.2 * G.1 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2, G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^3 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3^2 * G.2^-1 * G.3 * G.2^2 * G.3^-2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^4 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3 * G.2 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.3^-4 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-5 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.3^8 * G.2 * G.1 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-5 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 960 via triangle group [ 2, 4, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.1 * G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 880 via triangle group [ 2, 4, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-20 * G.1 * G.3^3 * G.2 * G.3^-7 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-7 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 880 via triangle group [ 2, 4, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-15 * G.1 * G.3^5 * G.2 * G.3^-1 * G.1 * G.3^6 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 864 via triangle group [ 2, 4, 54 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-35 * G.1 * G.3^9 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 101 action of group of order 840 via triangle group [ 2, 4, 84 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-17 * G.1 * G.3^9 * G.2 * G.1 * G.3^2 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 840 via triangle group [ 2, 4, 84 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-13 * G.1 * G.3^14 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3^7 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 832 via triangle group [ 2, 4, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.3^-86 * G.1 * G.3^7 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-5 ] Genus 101 action of group of order 832 via triangle group [ 2, 4, 104 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^4, (G.2 * G.3^-3)^2, G.3^-36 * G.1 * G.3^7 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 816 via triangle group [ 2, 4, 204 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-204 ] Genus 101 action of group of order 808 via triangle group [ 2, 4, 404 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^4, (G.2 * G.3^-1)^2, G.3^-53 * G.1 * G.2^-1 * G.3^-148 ] Genus 101 action of group of order 800 via triangle group [ 2, 5, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-1, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-2 * G.3^-1 * G.2 ] Genus 101 action of group of order 1200 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3^6, G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 1200 via triangle group [ 2, 6, 6 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3^6, G.1 * G.3 * G.2^-1 * G.3^2 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-2 * G.2 * G.3^-2 * G.2 * G.3^-1 ] Genus 101 action of group of order 960 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^3 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 960 via triangle group [ 2, 6, 8 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-3)^2, G.3^8, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 ] Genus 101 action of group of order 750 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2, G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-2 * G.3 ] Genus 101 action of group of order 750 via triangle group [ 2, 6, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1, (G.2^-2 * G.3)^5 ] Genus 101 action of group of order 672 via triangle group [ 2, 6, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, (G.2 * G.3^-1)^4, G.3^-8 * G.1 * G.3^5 * G.2 * G.1 * G.3^3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 672 via triangle group [ 2, 6, 28 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-1 * G.2)^2, G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 624 via triangle group [ 2, 6, 78 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^6, (G.2 * G.3^-2)^2, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2 * G.3^-6 * G.1 * G.3^2 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 606 via triangle group [ 2, 6, 303 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^6, G.3^83 * G.2 * G.1 * G.2^-1 * G.3^-9 * G.1 * G.3^7 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.3^2 * G.2^3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2^-2 * G.3 * G.2^-4 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is reflexible [n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-2 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3^3 * G.2^-1 * G.3^3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2^3 * G.1 * G.2^-3 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.2^8, (G.2 * G.3^-1)^4, G.3^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 2, 8, 8 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^8, G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2^2 * G.1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-2 * G.1 * G.3 * G.2 * G.1 * G.3^3 * G.2 * G.3^-1 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.1 * G.3 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3^2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.1, G.3^-3 * G.1 * G.3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.1 * G.3^2 ] Genus 101 action of group of order 640 via triangle group [ 2, 8, 16 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-2 * G.1 * G.2^-1 * G.3^-3 * G.1, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.2^-2 * G.3^-2 * G.2, G.3^-17 * G.1 * G.3^4 * G.2 * G.1 * G.3^2 * G.2 * G.3^-3 * G.1 * G.3 * G.2 * G.3^-6 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-1 * G.1 * G.3^10 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-13 * G.1 * G.3^2 * G.2 * G.1 * G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-3 * G.1 * G.3^3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.2^-1 * G.1 * G.3^4 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-3 * G.1 * G.3^3 * G.2 * G.3^-4 * G.1 * G.2^-2 * G.3^3 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-1)^4, G.3^3 * G.2^-2 * G.3^-2 * G.1 * G.2^-1, G.3^-3 * G.1 * G.3^3 * G.2^-2 * G.3 * G.2 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-8 * G.1 * G.3^4 * G.2 * G.1 * G.3^18 * G.2^-1 * G.3^-2 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 576 via triangle group [ 2, 8, 36 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2^-2 * G.3^-1 * G.1 * G.2^-1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, G.3^-11 * G.1 * G.3 * G.2 * G.3^-4 * G.1 * G.3^5 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-4 * G.1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 560 via triangle group [ 2, 8, 56 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.1 * G.3^6 * G.2 * G.1 * G.2^-1 * G.3^-6 ] Genus 101 action of group of order 560 via triangle group [ 2, 8, 56 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^6 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-5 * G.1 ] Genus 101 action of group of order 560 via triangle group [ 2, 8, 56 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^3 * G.2 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-6 * G.1 ] Genus 101 action of group of order 560 via triangle group [ 2, 8, 56 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^8, (G.2 * G.3^-1 * G.2^2)^2, (G.2 * G.3^-3)^2, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2^-1 * G.3^-6 ] Genus 101 action of group of order 544 via triangle group [ 2, 8, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.2^8, G.3^-31 * G.1 * G.3^20 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-3 * G.1 * G.3^2 * G.2^-1 * G.3^-7 ] Genus 101 action of group of order 544 via triangle group [ 2, 8, 136 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-1)^2, G.2^8, G.3^45 * G.2 * G.1 * G.3 * G.2 * G.3^-10 * G.1 * G.3^10 ] Genus 101 action of group of order 600 via triangle group [ 2, 10, 15 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2)^2, G.2^10, G.2^2 * G.3^-1 * G.2^4 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 600 via triangle group [ 2, 10, 15 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.2^10, (G.2 * G.3^-1 * G.2^3)^2, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-1 * G.3^-3, G.1 * G.2^-4 * G.3^-2 * G.2 * G.3^-1, G.2^12, G.1 * G.3 * G.2^2 * G.3^-1 * G.2^2 * G.1 * G.2^3 * G.3^-1 * G.2^2 * G.3^-1 * G.2 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^2, G.1 * G.3 * G.2^-4 * G.3^-3 * G.2 * G.3^-1, G.3^-1 * G.2^2 * G.1 * G.2^-2 * G.3^2 * G.2^-1 * G.3^-2, G.2^12 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3^2, G.3^-2 * G.1 * G.2^-3 * G.3 * G.2^-1 * G.3^-2 * G.2, G.1 * G.3^2 * G.2^-3 * G.3^-1 * G.2^2 * G.3^-2, G.2^12 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-4, G.2^12, G.3^2 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 600 via triangle group [ 2, 12, 12 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^12, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 ] Genus 101 action of group of order 480 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3, G.3^3 * G.2^-3 * G.3^-1 * G.1 * G.3 * G.2^-2 ] Genus 101 action of group of order 480 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3 * G.2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.2 * G.1 * G.3^2 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3^-1, G.2^-1 * G.3^2 * G.2^-3 * G.3^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 480 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-16 ] Genus 101 action of group of order 480 via triangle group [ 2, 16, 48 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-16 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^-1 * G.2, G.2 * G.3^-2 * G.2^3 * G.3^-1 * G.2 * G.3^-2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^2 * G.2^-1 * G.3^-1, G.2^6 * G.3^-2 * G.2 * G.3^-1 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-3 * G.2, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3, G.3^-1 * G.2^5 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, (G.3^-1 * G.2)^5 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.1, G.2 * G.3^-1 * G.2^4 * G.3^-1 * G.2^2 * G.3^-1 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2 * G.3^-2 * G.2^3 * G.3^-3 * G.2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^2 * G.3^-2 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^5 * G.3^-2 * G.2^2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-3 * G.3^-1 * G.2 * G.3^-1 * G.2, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-2 * G.2 * G.3^-1 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3^2 * G.2^-2 * G.3^-2 * G.2 * G.3^-1, G.2^6 * G.3^-1 * G.2 * G.3^-2 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.3^-2 * G.1 * G.2^-2 * G.3^-3 * G.2, G.1 * G.3^3 * G.2^-1 * G.3^-4, (G.3^-1 * G.2)^5 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.2^-1 * G.3 * G.2^-3 * G.3^-2 * G.1 * G.2^-1, (G.3^-1 * G.2)^5 ] Genus 101 action of group of order 500 via triangle group [ 2, 20, 20 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.2^4 * G.3^-3, (G.3^-1 * G.2)^5 ] Genus 101 action of group of order 480 via triangle group [ 2, 20, 30 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.1 * G.3^2 * G.2^-2 * G.3^-3 * G.2, G.3^-2 * G.2^4 * G.3^-4 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-4 * G.3 * G.2^-2 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-5 * G.3^-1 * G.1 * G.2^-1 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-2 * G.3 * G.2^-1 * G.3^2, G.2 * G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3 * G.2^-3 * G.3^-1 * G.1 * G.3^2, G.1 * G.2^-1 * G.3^2 * G.2^2 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-2 * G.2^2 * G.3^-1 * G.2 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-2 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2 * G.3^-2 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-2 * G.2 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.3 * G.2^-3 * G.3 * G.2^-1 * G.3^-2, G.3^-1 * G.2 * G.1 * G.2^-2 * G.3^-1 * G.2 * G.3^-2 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, (G.2 * G.3^-2 * G.2)^2, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-2 * G.2 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.2 * G.1 * G.3 * G.2^3 * G.1 * G.2^-1 * G.3^-1 * G.2, (G.3^-1 * G.2)^5, G.2^-1 * G.3 * G.2^-4 * G.3^-3 * G.2 * G.1 ] Genus 101 action of group of order 480 via triangle group [ 2, 24, 24 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3^-1 * G.1 * G.3 * G.2^2 * G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-1 * G.2^3 * G.3^-1 * G.2 * G.3^-2 ] Genus 101 action of group of order 448 via triangle group [ 2, 28, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.3 * G.2^-2 * G.3^-2 * G.2, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.3^3 * G.2^-1 * G.3^-4, G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-2 * G.2^6 * G.3^-1 * G.2^2 * G.3^-1 * G.2 * G.3^-4 * G.2^5 * G.3^-1 ] Genus 101 action of group of order 448 via triangle group [ 2, 28, 56 ] Action is reflexible [m] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-4 * G.3^-1 * G.2^3, G.1 * G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1 * G.2, G.2 * G.3^-1 * G.2 * G.3^-7 * G.2^3 * G.3^-1 * G.2^7 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-3 ] Genus 101 action of group of order 440 via triangle group [ 2, 44, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.3^-1 * G.2 * G.3^-23 * G.2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 440 via triangle group [ 2, 44, 44 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.2 * G.3^-1 * G.2^22 * G.3^-3 * G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 432 via triangle group [ 2, 54, 54 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-1 * G.2^2, G.2^2 * G.3^-37 * G.2^14 * G.3^-1 ] Genus 101 action of group of order 420 via triangle group [ 2, 84, 84 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1, G.2^2 * G.3^-21 * G.2 * G.3^-1 * G.2^8 * G.3^-1 * G.2 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 420 via triangle group [ 2, 84, 84 ] Action is chiral [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.2 * G.3^-1, G.3^-1 * G.2^20 * G.3^-4 * G.2 * G.3^-1 * G.2^9 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 416 via triangle group [ 2, 104, 104 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.1 * G.2^-2 * G.3^-1 * G.2, G.1 * G.3 * G.2^-1 * G.3^-2, G.3^-68 * G.2^36 ] Genus 101 action of group of order 416 via triangle group [ 2, 104, 104 ] Action is reflexible [m,n] [ G.1^2, G.3^-1 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1, G.1 * G.2^-3 * G.3^-3, G.2^2 * G.3^-1 * G.2^36 * G.3^-1 * G.2^9 * G.3^-2 * G.2 ] Genus 101 action of group of order 406 via triangle group [ 2, 203, 406 ] Action is reflexible [m] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^-1 * G.3^134 * G.2^-68 ] Genus 101 action of group of order 408 via triangle group [ 2, 204, 204 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^69 * G.3^-134 * G.2 ] Genus 101 action of group of order 404 via triangle group [ 2, 404, 404 ] Action is reflexible [m,n] [ G.1^2, G.1 * G.2^-1 * G.3^-1, G.3^-1 * G.2^-1 * G.1, G.2^68 * G.3^-133 * G.2 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1^-1 * G.3 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 101 action of group of order 2400 via triangle group [ 3, 3, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.1 * G.3 * G.2)^4, G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3 ] Genus 101 action of group of order 672 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^2 * G.2 * G.3^-2 ] Genus 101 action of group of order 672 via triangle group [ 3, 3, 28 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^-3, G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-2 * G.1 * G.3^5 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.1^-1 * G.2^-1 * G.3 * G.2^-2 * G.1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.1^-1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3^2 * G.2 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.2^-2 * G.1 * G.3^2 * G.2 * G.1^-1 * G.2^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.1^-1 * G.3 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.1^-1 * G.2^-1 * G.3^2 * G.2 * G.3^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is chiral [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3^2 ] Genus 101 action of group of order 1200 via triangle group [ 3, 4, 4 ] Action is reflexible [n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^4, G.3^4, G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3, (G.3^-1 * G.1^-1 * G.2^-1)^3, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.1^-1 ] Genus 101 action of group of order 600 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.1^-1 * G.2^-1 * G.1 * G.3, G.2^6, G.2^-2 * G.3^2 * G.2^-2 * G.3^2 * G.2^-1 * G.3 * G.2^-1 * G.3^2 * G.2^-2 * G.3^2 * G.2^-2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via triangle group [ 3, 6, 6 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^2 * G.1^-1 * G.3^2, G.2^6, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 101 action of group of order 480 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, G.2^3 * G.1^-1 * G.3^3, G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-2 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 3, 8, 8 ] Action is reflexible [m,n] [ G.1^-3, G.2^-1 * G.1^-1 * G.3^-1, (G.1 * G.3 * G.2)^2, G.2^3 * G.1^-1 * G.3^3, G.2^8 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-1, G.3 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.1 * G.3^2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2^2 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.2^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.3^-1 * G.1^-1 * G.2 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^2 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2^-1 * G.1 * G.3 * G.2^-1, G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.3 * G.1^-1 * G.2 * G.1^-2 * G.3 * G.2 * G.1^-1 * G.3 * G.2, G.1^-1 * G.2^-2 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3^2 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.1 * G.3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2, G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3^-1 * G.2)^2, (G.1 * G.2^-1)^4, G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2, G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1^-1 * G.3 * G.2)^2, (G.2 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.1 * G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, (G.1 * G.3 * G.2^-1)^2, (G.1 * G.3^-1)^4, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.2 * G.1, G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3 * G.2^2 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-2 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-2 * G.3^-1 * G.1 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, (G.3^-1 * G.1)^10 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2^-2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 101 action of group of order 800 via triangle group [ 4, 4, 4 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.1^2 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-2 * G.1 * G.2^-1 * G.1 * G.3^2 * G.2^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.1 * G.3 * G.2^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.1 * G.3^2 * G.2^-1 * G.1 * G.2^-1 * G.3^-2, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1, G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.1^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1, G.2 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^3 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1, G.3^-1 * G.1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4, G.1 * G.2^-1 * G.3^-1 * G.1^-2 * G.3 * G.2^-1 * G.3^-1 * G.2 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-1)^4, G.2 * G.1 * G.3^-1 * G.1^-2 * G.3 * G.2^2 * G.3^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^6, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.2 * G.1^-2 * G.3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1 * G.3^-1 * G.2 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via triangle group [ 4, 4, 6 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^6, G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.3 * G.2 * G.1^-2 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.2^-1 * G.1)^5 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3 * G.2 * G.1^-1 * G.2^-1)^2, (G.2^-1 * G.1)^5 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1, G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1, (G.1 * G.3^-1)^4 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^-2, G.2^-1 * G.3^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1^-1 * G.2 * G.1 * G.3, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.1^-1 * G.2^-1 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-2, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.3^-1, (G.1 * G.3^-1)^4 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3, G.3^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 500 via triangle group [ 4, 4, 10 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.2, G.3^-1 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.3^-1 * G.1^-1 * G.3 * G.2 * G.1 * G.3^2 * G.2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.2 * G.1^-1 * G.2 * G.1^2 * G.3^2 * G.1^-1, G.1^-1 * G.3^2 * G.2 * G.1 * G.2^-1 * G.3^-2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-2 * G.1^-1 * G.2^-1 * G.1 * G.3^2 * G.2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.1 * G.3^2 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1 * G.2)^2, G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.1 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.2, G.3^-3 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1 * G.3^-1 * G.1, G.3^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-2 * G.1^-1 * G.3, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^4 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3^-1 * G.2 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.1^-1 * G.2^-1, G.3 * G.2 * G.1 * G.3^2 * G.2 * G.3^-1 * G.1^-1 * G.3 * G.2 * G.1^-1 * G.3^4 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.3^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^2 * G.3^3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.1^-1 * G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.2 * G.1^-1 * G.2^-1 * G.3 * G.1^-1, G.2 * G.1 * G.3^-1 * G.1^-1 * G.2 * G.3^-2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3 * G.2 * G.1^-1 * G.3^2 * G.1^-1, G.2 * G.3^-2 * G.1^-1 * G.2 * G.1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.3 * G.2 * G.1^-1 * G.3 * G.2^2 * G.3^-1 * G.1 * G.3 * G.2^-1, G.3^-1 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.3^-3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3 * G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3^2 * G.2^-1 * G.3, G.1^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^-2 * G.2, G.3^-3 * G.1 * G.3 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1 * G.2^-1 * G.3^-4 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.3^-1 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2 * G.3^-1 * G.1, G.3^-3 * G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.3^2 * G.2 * G.1 * G.3^2 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-2 * G.3^3 * G.1^-1, G.1^-1 * G.2^-1 * G.3^-1 * G.1^-1 * G.2^-1 * G.1 * G.3^-1 * G.1 * G.3^2, G.3^-2 * G.1^-1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2^-1 * G.3^-1 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1^-1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-3 * G.1^-1 * G.2 * G.3^-2, G.3 * G.2^-1 * G.3 * G.2 * G.3^-1 * G.2 * G.1 * G.2^-1 * G.3^2 * G.2^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3^-2 * G.2)^2, G.3^-1 * G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.2 * G.1^-1 * G.2^-2 * G.1 * G.3 * G.2^-1 * G.3^-1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^-3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2)^2, G.3^3 * G.1^-1 * G.3^2 * G.2^-1, (G.1 * G.3 * G.1^-1 * G.2^-1)^2 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3 * G.1^-1 * G.3 * G.1^-1 * G.2^-1 * G.1 * G.3 * G.1^-1 * G.3 * G.1^-1 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 4, 4, 12 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^2 * G.2 * G.1^-1 * G.3^3, G.3^-1 * G.1 * G.3^-1 * G.1^-2 * G.2^-1 * G.1^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 440 via triangle group [ 4, 4, 22 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^6 * G.2^-1 * G.3^-4 * G.1^-1 * G.3 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 101 action of group of order 440 via triangle group [ 4, 4, 22 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^6 * G.2^-1 * G.3^-4 * G.1^-1 * G.3 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 101 action of group of order 432 via triangle group [ 4, 4, 27 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^-1 * G.3^-1 * G.2 * G.1^-1 * G.3 * G.2^-1 * G.3, G.3^-10 * G.1^-1 * G.3^4 * G.2 * G.1^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.3^-8 ] Genus 101 action of group of order 432 via triangle group [ 4, 4, 27 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3 * G.2 * G.1^-2 * G.3^2 * G.1^-1, G.3^8 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.1^-1 * G.2 * G.3^-1 * G.1^-1 * G.3^9 ] Genus 101 action of group of order 432 via triangle group [ 4, 4, 27 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.1^2 * G.3 * G.2^-1, G.2 * G.1^-1 * G.2^-1 * G.1 * G.3^-2, (G.1 * G.3^-1 * G.2)^2, G.3^-13 * G.1 * G.3^5 * G.2 * G.1 * G.3^4 * G.2 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 420 via triangle group [ 4, 4, 42 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.1^-1 * G.2 * G.1^-2 * G.2^-1 * G.3^-1 * G.2, G.3^9 * G.2 * G.1 * G.3 * G.2 * G.3^-9 * G.1^-1 ] Genus 101 action of group of order 420 via triangle group [ 4, 4, 42 ] Action is chiral [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, G.3 * G.1^-1 * G.2 * G.1^-1 * G.2^2 * G.1, G.3^6 * G.2^-1 * G.3^-3 * G.1^-1 * G.3 * G.2 * G.3^-9 * G.1^-1 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^38 * G.2^-1 * G.3^-4 * G.1 * G.2^-1 * G.3^-8 * G.1 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.2 * G.3^-1)^2, G.2 * G.1^-2 * G.3 * G.1^-1, G.3^-41 * G.1^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^5 * G.2 * G.3^-2 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3^-1)^2, G.3^-1 * G.2 * G.1^-1 * G.2^2, G.3^44 * G.2^-1 * G.1 * G.2^-1 * G.3^-6 * G.1 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.3^2 * G.1^-1 * G.3 * G.2^-1, (G.1 * G.3^-1 * G.2)^2, G.3^10 * G.2 * G.3^-4 * G.1^-1 * G.2 * G.1^-1 * G.2 * G.3^-7 * G.1 * G.3^2 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^3 * G.2^-1 * G.3^-1 * G.1^2 * G.3^4 * G.2^-1 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.1^-1 * G.3 * G.2^-1 * G.3^9 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, (G.1 * G.3 * G.2^-1)^2, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, G.3^-4 * G.2 * G.1^2 * G.3^3 * G.2 * G.3^-1 ] Genus 101 action of group of order 416 via triangle group [ 4, 4, 52 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^4, G.3 * G.2^-1 * G.3 * G.2^-1 * G.3^-3 * G.1^2 * G.3^5 ] Genus 101 action of group of order 408 via triangle group [ 4, 4, 102 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^86 * G.2^-1 * G.1^-1 * G.3^15 ] Genus 101 action of group of order 408 via triangle group [ 4, 4, 102 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.3^-3 * G.2 * G.1^2 * G.3^2 * G.2 * G.3^-1 ] Genus 101 action of group of order 408 via triangle group [ 4, 4, 102 ] Action is reflexible [n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^4, G.2^-1 * G.3^-1 * G.2 * G.1 * G.3 * G.1^-1, (G.1 * G.3^2 * G.2^-1)^2, G.2 * G.3^-2 * G.2 * G.1^2 * G.3^4 ] Genus 101 action of group of order 404 via triangle group [ 4, 4, 202 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.3 * G.1^-1 * G.2^-1, G.1^4, G.3^85 * G.2^-1 * G.1 * G.3^15 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, G.2^-1 * G.3^-1 * G.2^2 * G.1^-1 * G.3 * G.2^-2 * G.3 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m,n] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2 * G.1^-2 * G.3 * G.1^-1, G.2^6, G.3^6, (G.2 * G.3^-2 * G.2)^2 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3 * G.1^-1 * G.2 * G.1^2 * G.3 * G.2 * G.1^-1, G.3 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.2^-2, (G.1^-1 * G.3 * G.2^2)^2 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.2^-1)^2, G.2^6, G.3^6, (G.2 * G.3^-2 * G.2)^2 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m] and there is a non-orientable quotient [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, G.2^6, (G.1 * G.3 * G.2)^2, G.3^6, G.3 * G.1^-1 * G.2 * G.1^2 * G.2^-1 * G.3^-1 * G.1, (G.1 * G.2^-1)^4, (G.1 * G.3 * G.2^-2)^2 ] Genus 101 action of group of order 480 via triangle group [ 4, 6, 6 ] Action is reflexible [m] [ G.2^-1 * G.1^-1 * G.3^-1, G.1^4, (G.1 * G.3^-1)^2, G.2^6, G.3^6, (G.2 * G.3^-2 * G.2)^2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, (G.3 * G.1 * G.2 * G.1)^4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3)^6, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.2)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.3)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3, (G.1 * G.2)^6, G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.2)^6, G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, (G.1 * G.2)^6, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 1200 via quadrangle group [ 2, 2, 2, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^50 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4, (G.1 * G.3)^50 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^2 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1^2 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3)^10 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^10 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4^-1)^4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3)^4, G.2 * G.4^2 * G.1 * G.4^2 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4 * G.3 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^4, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^2 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.2)^4, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.2 * G.4^-2 * G.2 * G.4^2, (G.2 * G.1)^5, G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.3 * G.1)^5 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.2 * G.1)^5, (G.3 * G.1)^5, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^5, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, (G.3 * G.1)^5 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, (G.2 * G.1)^5, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, (G.3 * G.1)^5, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 800 via quadrangle group [ 2, 2, 2, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.4^2, G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.2)^4, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1, G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1^2 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.1, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4 * G.2 * G.1 * G.4, G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^10, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^10, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^10, G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^10, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, G.4^6, (G.1 * G.3)^4, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.1 * G.4^-2 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.4^-2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^6, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.4^-2 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.2 * G.4^2 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^3, G.4^6, G.4 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4^6, G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2)^3, (G.1 * G.3)^6, G.4 * G.2 * G.4^-2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-2 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^2 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, (G.3 * G.1)^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.3 * G.1)^3, G.4^6, G.4^-2 * G.3 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.4 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, (G.4^-1 * G.2)^3, G.4^6, G.2 * G.4^-1 * G.3 * G.1 * G.4 * G.2 * G.4^-3 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, G.4^6, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.4^6, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, (G.1 * G.2)^4, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.4^6, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.4^-3 * G.2 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-2 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.1)^5, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.3)^2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^6, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5, (G.1 * G.4 * G.2 * G.4^-1 * G.2)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^6, (G.1 * G.4^2 * G.3)^2, (G.2 * G.1)^5, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^6, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, (G.1 * G.4 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.2 * G.1)^5, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-3 * G.2 * G.4^3, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.1)^5, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.1)^5, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.2 * G.1)^5, (G.3 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, (G.2 * G.1)^5, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, (G.2 * G.4 * G.3 * G.4^-1)^2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.3 * G.1)^5, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^6, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.3 * G.1)^5, G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.3 * G.1)^5, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4 * G.3 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.1)^5, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.2, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, (G.1 * G.2)^6, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.1 * G.3)^6, G.3 * G.2 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, (G.1 * G.3)^6, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, (G.2 * G.1)^10 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, (G.1 * G.3 * G.1 * G.2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^6, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.3 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^6, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4^-2 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^6, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2, (G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.2)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^2 * G.3 * G.1 * G.4^3, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4^6, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.2 * G.4^2 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2, G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^6, (G.1 * G.2)^10, G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 2, 6 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^6, G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3, G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^10, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^2 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4 * G.3 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^2 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^10, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.4^2, (G.3 * G.1)^25 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^10, G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^10, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^2 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^5, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^10, G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1^2 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^10, G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^10, G.3 * G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^10, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^10, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^2 * G.2 * G.1 * G.4^2, G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-2 * G.1 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, (G.2 * G.1)^5, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.2 * G.1)^5, G.4^10, G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.4^2 * G.3 * G.2 * G.4^-3, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4^-3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-2 * G.1 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-2 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1, (G.3 * G.1)^5 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^10, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^5, G.4^10, G.4 * G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^10, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2, (G.1 * G.4 * G.2 * G.4 * G.2)^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.4 * G.3 * G.4^-1)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.4^-2 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.2 * G.1)^5, G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, (G.3 * G.1)^5, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.2 * G.4^-2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.3 * G.1)^5, (G.4^-1 * G.2)^5 ] Genus 101 action of group of order 500 via quadrangle group [ 2, 2, 2, 10 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.2 * G.1)^5, G.4 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, (G.1 * G.3)^10 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^12, G.4 * G.2 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^2, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.3 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-3 * G.3 * G.4^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, (G.1 * G.3)^10 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1^2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, (G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.1^2 * G.4^6, G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3, (G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^12, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^12, G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^12, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^6 * G.1^2 * G.4^6, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.2 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.4^-1 * G.1 * G.2 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^12, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^12, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-3, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2, G.1 * G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.1 * G.4^-6, G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.3 * G.4^-4 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^4, (G.1 * G.3)^10 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^12, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, (G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.3 * G.1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-5, G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, (G.1 * G.3)^10 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, (G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.3 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^12, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^12, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^12, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^12, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^3 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^12, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.4 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^3, G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.4^-1 * G.1 * G.4^5 * G.1^2 * G.3 * G.1 * G.4 * G.3 * G.4^-3, G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^12, G.1 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2, G.4^-1 * G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1, G.4^-3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^3 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-2 * G.2, (G.1 * G.4 * G.2)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.2)^4, G.4^3 * G.3 * G.1 * G.4 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^3 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.3)^4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^3 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^6, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4 * G.3 * G.4^-3 * G.1 * G.4^-1 * G.2 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^6, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^3 * G.2 * G.1 * G.3 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.2)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^2 * G.3, (G.2 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3)^4, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.4^-1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^-1)^4, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, (G.1 * G.3)^4, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.1 * G.4^-4 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, (G.1 * G.2)^4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.4^-2 * G.2, G.4^-2 * G.1 * G.4 * G.3 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.3 * G.4^-2, G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-2 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.3)^4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.4^-1 * G.2)^2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3, G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^3 * G.1 * G.3 * G.1 * G.4^-3 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^2 * G.3 * G.1 * G.4^2 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4, G.4^-2 * G.2 * G.4^-2 * G.2 * G.1 * G.4 * G.2 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.3, G.4^-2 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.4 * G.2 * G.4 * G.3 * G.1 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.2 * G.1)^5 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.1)^5 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, (G.1 * G.4 * G.2 * G.1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^-3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.3)^4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, (G.2 * G.4^-1)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.2)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-2 * G.2, (G.1 * G.2)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1, G.4^-4 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.4^-5 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2, G.1 * G.3 * G.4^-3 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.3 * G.1 * G.4)^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.4^-4 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1 * G.4)^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, (G.1 * G.3 * G.4^-1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1, G.1 * G.4^3 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.4^-1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, (G.1 * G.4^2 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.2 * G.4 * G.1 * G.3 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.3, (G.1 * G.3)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^-1, (G.2 * G.4^-1)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.3)^6 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4, G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-2, G.4^12 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.1)^5, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-2 * G.2 * G.1 * G.2 * G.4^2 * G.3 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.2 * G.1)^5, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, (G.1 * G.4^2 * G.3)^2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, (G.1 * G.4^2 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.1, (G.1 * G.4^2 * G.3)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.4^-1 * G.2)^3, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, (G.1 * G.4^2 * G.2)^2, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-2 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^-2, (G.1 * G.4 * G.3 * G.1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.4^2 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4^-2 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, (G.3 * G.1)^5, G.4^2 * G.2 * G.4 * G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^2 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.1 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.1 * G.4^2 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4^2 * G.2)^2, (G.1 * G.4^2 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-2 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1 * G.3, G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.4^-2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-2 * G.1 * G.4, G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.3 * G.2, G.2 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-3 * G.2 * G.4^3, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.3 * G.1 * G.4^-2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^2 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.2)^4, G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.4^3, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.2 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.2, G.1 * G.4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.1 * G.3)^4, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4 * G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.3 * G.2 * G.4^-3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3)^4, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.4^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^-2 * G.2, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.2, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, (G.1 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3 * G.2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.2 * G.4, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.1 * G.4 * G.3)^2, G.4^3 * G.2 * G.1 * G.4 * G.2 * G.4, G.2 * G.4^-1 * G.3 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.2, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.2 * G.4^-3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^3, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.1 * G.4^2 * G.2 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-2)^2, G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.3 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^3 * G.2 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, (G.1 * G.4^2 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, (G.2 * G.4^-3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^2 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2, (G.2 * G.4^-2)^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, (G.2 * G.4^-3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.4 * G.3 * G.1 * G.2 * G.1 * G.4^4, G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.1, G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.4^3 * G.2 * G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3 * G.1 * G.2)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.4^-1 * G.2)^3, G.3 * G.1 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4^3, G.2 * G.4^-3 * G.2 * G.4^3, G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^3 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.4^-1 * G.2)^3, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^2 * G.2, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4, G.4^2 * G.2 * G.4^-1 * G.2 * G.4^2 * G.2, G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4^2 * G.2)^2, G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^-2 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.1 * G.3 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.4^-4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.1 * G.4^-2 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.1, G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.4^-1 * G.2)^3, G.2 * G.4^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.1, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.3 * G.1)^3, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-2 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.2 * G.4 * G.3 * G.4^-1)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.4^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.2, G.3 * G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4^2 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.2 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.4^2 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.4 * G.2, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4^2 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-2 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.4^3 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.4^-2, (G.2 * G.4^-2)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.3 * G.2 * G.4^-2, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.4^-1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4^3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-2 * G.1 * G.3 * G.1 * G.4^2 * G.3, (G.1 * G.4 * G.2 * G.1 * G.2)^2, G.4 * G.2 * G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, (G.1 * G.4^2 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, (G.2 * G.4^-3)^2, G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, G.4 * G.3 * G.1 * G.3 * G.2 * G.4^3, (G.2 * G.4 * G.3 * G.4^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^3 * G.3 * G.2 * G.4 * G.2 * G.4, (G.2 * G.4^2 * G.3 * G.4^-1)^2, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-2)^2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.1 * G.4 * G.2 * G.1 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4 * G.2 * G.1 * G.4^2 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.2 * G.4^-2)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.1 * G.3 * G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 2, 12 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.1)^3, (G.1 * G.4 * G.3)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.3 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-3 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^-3 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4^4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.2 * G.4^4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^3 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.4^4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^5, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^5 * G.3 * G.1 * G.2 * G.1 * G.4^5, G.2 * G.4 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4^-2 * G.2 * G.4 * G.1 * G.4 * G.1 * G.4 * G.1 * G.3 * G.4^-4 * G.2 * G.3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.3 * G.4^-2 * G.2 * G.3 * G.1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.4^4 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.2 * G.4^3 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.4^6 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^22, G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^5 * G.3 * G.1 * G.4^5, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4^4 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.4^4 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 * G.4^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-5 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3, G.1 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2, G.3 * G.4^-3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.1 * G.4^2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1, G.4^5 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.4^3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.4^5 * G.2 * G.1 * G.4^5, G.4^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^4 * G.2 * G.4^-1 * G.1 * G.4^5, G.1 * G.3 * G.4 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^-5 * G.1 * G.3 * G.1 * G.4^-6, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^-1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^4 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4, G.4^-9 * G.2 * G.4^2 * G.3 * G.4^-2 * G.2 * G.4 * G.1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^11 * G.3 * G.4^-4 * G.2 * G.3 * G.2 * G.1 * G.3 * G.2 * G.4^4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-2 * G.2 * G.3 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.2, G.4^4 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-1 * G.2 * G.4^12 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-4 * G.2 * G.4 * G.3 * G.1^2 * G.4^-11 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-7 * G.2 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^2 * G.3 * G.4^-9 * G.2 * G.4^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-3 * G.1 * G.4^4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4^22 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.3 * G.1 * G.3 * G.1 * G.2)^2, G.4^16 * G.3 * G.1 * G.4 * G.1^2 * G.3 * G.1 * G.4^3 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^22 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-2 * G.1 * G.4 * G.2 * G.4^6 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.4^-6 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^12 * G.3 * G.1 * G.3 * G.1^2 * G.4^-7 * G.1 * G.4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.4^-2 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-5 * G.1 * G.3 * G.4^7 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^2 * G.2 * G.4^-6 * G.1 * G.4 * G.2 * G.1 * G.4^11 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-9 * G.1 * G.4^5 * G.2 * G.1 * G.2 * G.4^-6 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^2 * G.2 * G.4^-4 * G.1 * G.4^3 * G.2 * G.4^-1 * G.1 * G.2 * G.1^2 * G.4^-5 * G.1 * G.3 * G.4^4 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-7 * G.3 * G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-2 * G.1 * G.3 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 440 via quadrangle group [ 2, 2, 2, 22 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.2 * G.4 * G.2 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4, G.4^-8 * G.1 * G.4 * G.2 * G.1 * G.4 * G.2 * G.4^-10 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.4^-1, G.4^-13 * G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4^2 * G.3 * G.4^-3 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.2)^4, G.4^15 * G.3 * G.4^-5 * G.2 * G.1^2 * G.3 * G.2 * G.4^5 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-13 * G.2 * G.1 * G.3 * G.4^-13 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, (G.1 * G.2)^4, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^16 * G.3 * G.4^-4 * G.2 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^4 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4 * G.3 * G.1 * G.4^-2, (G.1 * G.2)^4, G.4^27 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-20 * G.1^2 * G.4^-7 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^14 * G.2 * G.4^-6 * G.1 * G.4^2 * G.2 * G.1 * G.4^3 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^14 * G.2 * G.4^-4 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^4 ] Genus 101 action of group of order 432 via quadrangle group [ 2, 2, 2, 27 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.2)^2, G.4^-19 * G.1 * G.4 * G.3 * G.2 * G.1 * G.2 * G.1 * G.4^2 * G.2 * G.4^-2 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.2 * G.4^7 * G.3 * G.4^-1 * G.2 * G.1 * G.3 * G.4^-11 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4^15 * G.1 * G.4^6 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^8 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.3 * G.4^-4 * G.2 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^6 * G.3 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1^2 * G.4^-1 * G.1 * G.4^-9 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2 * G.4^4 * G.3 * G.4^-4 * G.1 * G.2 * G.3 * G.2 * G.4^4 * G.3 * G.2 * G.4 * G.3 * G.4^-2 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.1 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.1 * G.4, G.4^-8 * G.2 * G.4^6 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, (G.1 * G.2 * G.1 * G.3 * G.1 * G.3)^2, G.4^13 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^-8 * G.1 * G.4 * G.1 * G.4^-5 * G.1 * G.4^3 * G.3 * G.4^-3 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^14 * G.1^2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4^2 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2, G.4^15 * G.3 * G.1 * G.4^5 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4, G.4 * G.3 * G.4^-7 * G.2 * G.4^-5 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^6 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1, G.4^-3 * G.1 * G.4^7 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-7 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4 * G.2 * G.4^-8 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4^9 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^3 * G.2 * G.4^-4 * G.1 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^5 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.1 * G.4^4 * G.3 * G.4^2 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.2)^2, G.2 * G.4^-1 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1, G.4^-8 * G.1 * G.4^5 * G.1^2 * G.4^6 * G.2 * G.4^-1 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.2 * G.4^-7 * G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.4^10 ] Genus 101 action of group of order 420 via quadrangle group [ 2, 2, 2, 42 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4, G.4^14 * G.2 * G.1 * G.4^6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, (G.1 * G.3)^4, G.4^-52 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4^36 * G.3 * G.4^-1 * G.2 * G.1^2 * G.3 * G.4^-13 * G.2 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^42 * G.3 * G.1 * G.3 * G.4^-7 * G.1 * G.4 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^27 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.4^13 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, (G.1 * G.2)^4, G.4^-34 * G.2 * G.4^-1 * G.1 * G.4^8 * G.3 * G.4^-8 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-33 * G.1 * G.2 * G.1 * G.2 * G.4^-4 * G.1 * G.3 * G.4^5 * G.2 * G.4^-7 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^10 * G.3 * G.4^-5 * G.2 * G.4^2 * G.3 * G.4^-6 * G.2 * G.4 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^14 * G.3 * G.4^-1 * G.2 * G.4 * G.1 * G.4 * G.3 * G.4^-1 * G.2 * G.4^3 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^13 * G.3 * G.1 * G.4 * G.2 * G.4^11 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^6 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4^9 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.4^-6 * G.1 * G.2 * G.4^11 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^6 * G.2 * G.1 * G.4^2 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4^10 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1, G.4^16 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^4 * G.3 * G.2 * G.4^3 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.2, G.4^-14 * G.2 * G.4^5 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3 * G.4^-2 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.1 * G.3)^4, G.4^13 * G.3 * G.2 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.4^5 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.1 * G.4 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.2 * G.4^11 * G.1 * G.4 * G.1^2 * G.3 * G.4^-13 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.4 * G.3 * G.2 * G.4^2, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2, G.1 * G.4^4 * G.2 * G.4 * G.2 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-15 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.4^13 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.4^9 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.4 * G.2 * G.4^-9 * G.1 * G.4 * G.2 * G.1 * G.4^13 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is chiral [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.2 * G.4^-1)^2, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3)^4, G.4^-9 * G.1 * G.4^3 * G.2 * G.4^-5 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-5 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4^-4 * G.1 * G.4^3 * G.3 * G.4^-4 * G.1 * G.4^5 * G.1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2, G.4^-7 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.4^8 * G.3 * G.4^-8 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, (G.1 * G.3 * G.1 * G.2)^2, G.4 * G.2 * G.4^-10 * G.1 * G.2 * G.1 * G.2 * G.1 * G.4^6 * G.3 * G.4^6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4 * G.2, G.4^4 * G.2 * G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.1 * G.4^14 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^23 * G.3 * G.4^-1 * G.2 * G.4^19 * G.1^2 * G.3 * G.4^-1 * G.2 * G.4^6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^52 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^23 * G.2 * G.4^-1 * G.1 * G.4^19 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, (G.1 * G.2)^4, (G.1 * G.3)^4, G.4^11 * G.1 * G.4^4 * G.3 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.3 * G.4^-3 * G.2 * G.4^3 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1,2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, G.1 * G.4 * G.3 * G.2 * G.4^2, (G.1 * G.2)^4, G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4, G.4^8 * G.3 * G.4^-5 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, (G.1 * G.3)^4, G.4^-8 * G.3 * G.4^-6 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^8 * G.2 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.3, G.3 * G.4^-3 * G.2 * G.4 * G.3 * G.4^-19 * G.2 * G.4 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.4 * G.2)^2, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, G.4^-7 * G.2 * G.4^6 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4 * G.3 * G.4^-9 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.4^-21 * G.1 * G.3 * G.1 * G.3 * G.4^-3 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4, G.3 * G.4^-21 * G.2 * G.1^2 * G.4^-1 * G.1 * G.4^3 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4, G.4^5 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^6 * G.3 * G.1 * G.3 * G.4^-6 * G.1 * G.4^6 ] Genus 101 action of group of order 416 via quadrangle group [ 2, 2, 2, 52 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.1 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.3, G.4^4 * G.2 * G.4^-1 * G.1 * G.4 * G.1^2 * G.2 * G.4^-17 * G.1 * G.4 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4 * G.3 * G.4^-27 * G.2 * G.4 * G.3 * G.1 * G.4^-20 * G.2 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1, (G.1 * G.2)^4, G.4^-28 * G.2 * G.4 * G.3 * G.4^-21 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^-45 * G.1 * G.3 * G.4^-5 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [2] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4, G.3 * G.1 * G.2 * G.1 * G.3 * G.2, G.4^43 * G.3 * G.4^-1 * G.1 * G.4^6 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^22 * G.2 * G.4^-1 * G.1 * G.4^18 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^4, G.4^43 * G.2 * G.4^-1 * G.1 * G.4^6 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.1 * G.3 * G.4^-2, G.4^-17 * G.1 * G.4^-2 * G.1 * G.4^-15 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.1 * G.4^2 * G.2 * G.1 * G.2 * G.4^-2, G.4^-19 * G.2 * G.3 * G.4^-1 * G.1 * G.4^-13 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.1 * G.4^-1 * G.1 * G.4, G.1 * G.4^2 * G.3 * G.2 * G.4^3, G.4^-2 * G.1 * G.4^2 * G.3 * G.1 * G.3 * G.1 * G.4^12 * G.3 * G.4^-12 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, (G.2 * G.4^-1)^2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^8 * G.2 * G.4^-12 * G.1 * G.2 * G.4^-1 * G.1 * G.4^11 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-2 * G.1 * G.2 * G.1 * G.4^2 * G.2, G.4^7 * G.3 * G.4^-2 * G.2 * G.4^-6 * G.2 * G.4^-5 * G.1 * G.2 * G.4^8 * G.2 * G.4^2 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.4^-3 * G.2 * G.1 * G.4^2 * G.3, G.4^7 * G.2 * G.4^-1 * G.1 * G.2 * G.4^-6 * G.3 * G.4^-5 * G.1 * G.2 * G.1 * G.4 * G.2 * G.1 * G.4^4 * G.2 * G.1 * G.3 * G.4^4 * G.2 * G.1 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-102 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1,2] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^-92 * G.2 * G.1 * G.3 * G.4^-9 ] Genus 101 action of group of order 408 via quadrangle group [ 2, 2, 2, 102 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^-102 ] Genus 101 action of group of order 404 via quadrangle group [ 2, 2, 2, 202 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, (G.1 * G.3)^2, G.4^-50 * G.2 * G.3 * G.4^-50 ] Genus 101 action of group of order 404 via quadrangle group [ 2, 2, 2, 202 ] Action is reflexible [1,2] and there is a non-orientable quotient [2] [ G.1^2, G.2^2, G.3^2, (G.1 * G.2)^2, G.3 * G.2 * G.1 * G.4^-1, G.1 * G.3 * G.2 * G.4, G.4^91 * G.3 * G.1 * G.4^9 ] Genus 101 action of group of order 404 via quadrangle group [ 2, 2, 2, 202 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^2, G.3 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, (G.1 * G.3)^2, G.4^93 * G.2 * G.1 * G.4^7 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1)^6, (G.3 * G.1 * G.3^-1 * G.1)^10, G.2 * G.1^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4 * G.2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1, G.4 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4, G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.3, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.4 * G.2, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.2 * G.4, G.4^-3, G.4^-1 * G.1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.3^-1, G.4^-1 * G.3 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2, (G.1 * G.3 * G.2 * G.3^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3, G.2 * G.4^-1 * G.1 * G.4 * G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2, G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4^-1, G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1 * G.4, G.4^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.3^-1 * G.1 * G.4 * G.3^-1, (G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1)^2, G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.3, G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.2 * G.4^-1, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.1 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.2 * G.4^-1)^2, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4 * G.3^-1 * G.1 * G.3^-1 * G.2, G.4^-1 * G.3^-1 * G.4^-1 * G.3^-1 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.4^-1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4, (G.1 * G.4 * G.3)^2, G.1 * G.4^-1 * G.1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 * G.3^-1, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.1 * G.2 * G.1 * G.3^-1 * G.1, (G.1 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.2, G.2 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.4^-1, G.2 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.2 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.1 * G.4 * G.2 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 * G.1, G.1 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.2 * G.4 * G.2 * G.4^-1)^2, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.2 * G.4^-1, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.4 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.4 * G.3 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4^-1 * G.2, G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.1 * G.3^-1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1, G.1 * G.3^-1 * G.2 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3 * G.1 * G.3^2 * G.1 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, (G.2 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3, G.2 * G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.4 * G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3^-1 * G.1 * G.3 * G.4^-1, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1, G.3 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1, (G.1 * G.4 * G.2 * G.4^-1)^2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.2 * G.3^-1)^2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.3^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.3 * G.2, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.4, G.2 * G.4 * G.2 * G.1 * G.2 * G.1 * G.3 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2 * G.1 * G.3 * G.2 * G.3^-1, G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4^-1 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^-3, G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.2, G.3 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.3 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1, G.1 * G.3 * G.4^-1 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4, G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.1 * G.4 * G.3)^2, (G.2 * G.4 * G.3)^2, G.2 * G.4 * G.2 * G.1 * G.3^-1 * G.1 * G.4, G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.4^-1 * G.3^-1, G.3^-3, (G.3^-1 * G.1 * G.3 * G.1)^3, (G.3^-1 * G.1)^20, G.2 * G.1^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.2 * G.4^-1)^4, G.3 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, (G.2 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.4^-1 * G.2 * G.3^-1 * G.4 * G.2 * G.4^-1 * G.2 * G.3 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.4 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4 * G.2 * G.4, G.1 * G.2 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.2 * G.4^-1 * G.2)^2, G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.4^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3^-1 * G.1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1 * G.1 * G.2)^2, G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.3, (G.2 * G.4^-1)^4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, (G.4^-1 * G.3)^3, (G.1 * G.3^-1)^4, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, (G.1 * G.2)^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1, G.1 * G.4 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.3, G.3^-1 * G.1 * G.4 * G.2 * G.3 * G.2 * G.4^-1 * G.2 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4^-1 * G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3^-1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.3 * G.2 * G.4 * G.1 * G.3^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^-3, G.2 * G.3^-1 * G.1 * G.3 * G.4^-1, G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.3^-1 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 * G.3^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is reflexible [1,3] and there is a non-orientable quotient [3] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.4, G.4 * G.3^-1 * G.1 * G.4 * G.2, G.2 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.4, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, (G.1 * G.3^-1)^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.4^-1 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^-3, G.4^-1 * G.3 * G.1 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4 * G.3^-1 * G.4^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.2 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.4^-1 * G.1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, G.4 * G.3^-1 * G.4 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.2, G.1 * G.3^-1 * G.4^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.4 * G.2 * G.3^-1 * G.1 * G.4^-1 * G.2 * G.4^-1, (G.2 * G.4^-1)^4, G.3 * G.2 * G.3 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.2 * G.4^-1, G.3^-3, (G.2 * G.1)^3, G.4^-1 * G.3 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.1 * G.3^-1 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.4^-1 * G.3 * G.1 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 2, 3, 3 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^-3, (G.2 * G.1)^3, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.4^-1 * G.1 * G.4, G.4 * G.3 * G.2 * G.4 * G.3 * G.2 * G.4 * G.3^-1 * G.4 * G.3^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.4^-1 * G.2 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.3^-1 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.4^-1 * G.3, G.2 * G.3 * G.2 * G.3^-1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.3 * G.1 * G.3^-1 * G.1 * G.2 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.2 * G.4^-1 * G.2)^2, (G.1 * G.3 * G.1 * G.3^-1)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.1 * G.4 * G.3^-1)^2, (G.1 * G.3^-1 * G.1 * G.2)^2, G.1 * G.3 * G.2 * G.3^-1 * G.1 * G.4 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, (G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3^-1, G.2 * G.4^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4, (G.1 * G.3^-1 * G.4 * G.3^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.1 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.3 * G.1 * G.2 * G.1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, (G.1 * G.2)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.1 * G.3, G.3^-3, G.4^4, G.2 * G.4 * G.3^-1 * G.1 * G.4 * G.3^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.1 * G.3^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.3 * G.2 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.1 * G.3^-1, (G.3 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.2 * G.3 * G.2 * G.1 * G.2 * G.4, G.3 * G.1 * G.3^-1 * G.1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, (G.2 * G.4 * G.3)^2, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.3^-1 * G.4 * G.3, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4, G.1 * G.3^-1 * G.4 * G.3^-1 * G.2 * G.3^-1 * G.4^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, (G.1 * G.2)^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.3^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.1 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.3, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.1 * G.3^-1 * G.2 * G.4, G.3^-3, G.4^4, G.4^-1 * G.1 * G.2 * G.1 * G.4 * G.2, G.2 * G.1 * G.3^-1 * G.4 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3^-1 * G.1 * G.2 * G.4^-1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, (G.1 * G.3^-1)^2, G.3^-3, G.4^4, G.4 * G.3^-1 * G.4^-1 * G.1 * G.4^-1 * G.2 * G.3^-1, G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is reflexible [1] [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.2 * G.3^-1 * G.1 * G.4^-1, G.3^-3, G.4^4, G.1 * G.3^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, G.1 * G.4 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1, G.1 * G.4 * G.1 * G.3^-1 * G.2 * G.3^-1 * G.2 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, G.4^4, G.4^-2 * G.2 * G.1 * G.4 * G.3, (G.2 * G.4 * G.3)^2, (G.1 * G.3 * G.1 * G.3^-1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 2, 3, 4 ] Action is chiral [ G.1^2, G.2^2, G.3^-1 * G.2 * G.1 * G.4^-1, G.3^-3, (G.2 * G.4^-1)^2, G.4^4, G.4^-1 * G.1 * G.3^-1 * G.1 * G.3^-1 * G.4 * G.3^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.1 * G.3 * G.1 * G.4 * G.3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3, G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2, G.1 * G.3 * G.1 * G.4 * G.1 * G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^-3, G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 * G.4 * G.2 * G.4 * G.2 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.3 * G.1 * G.2 * G.4, G.4 * G.1 * G.2 * G.3, G.4^-3, G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.1 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.3 * G.1 * G.2 * G.4 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.1 * G.3 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.1 * G.4, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2, G.4^-1 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2, G.4 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.1 * G.2^-1 * G.3)^3, (G.1 * G.3)^10 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4^-1 * G.2^-1, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.2 * G.3 * G.1 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.4 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.2^-1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2)^3, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1, G.3 * G.1^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4, G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.3 * G.4^-1, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, (G.2^-1 * G.4^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 * G.3, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4, G.1 * G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.2 * G.1 * G.2^-1 * G.3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.4^-1 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3, G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4, G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1, G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.4 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.4, G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.3 * G.4^-1 * G.1 * G.4, G.4^-3, G.1 * G.3 * G.1 * G.3 * G.4 * G.2 * G.4 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1, (G.1 * G.2^-1 * G.3)^3, G.3 * G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1, G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.3 * G.1 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.4 * G.3, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4 * G.2 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.4^-1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.1, G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1, G.1 * G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^-3, G.4 * G.2 * G.3 * G.1 * G.3 * G.2^-1 * G.4^-1 * G.1 * G.4 * G.2 * G.4 * G.2 * G.4 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1, G.3 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2 * G.3 * G.2^-1 * G.3)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4, G.1 * G.4 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.4 * G.2 * G.4 * G.2 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.2 * G.3, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4 * G.3 * G.4^-1, G.3 * G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.2, G.4 * G.2 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, (G.2^-1 * G.4^-1 * G.1)^2, G.4^-1 * G.3 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.4^-1 * G.1 * G.4 * G.3 * G.1 * G.3 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.3 * G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.2^-1 * G.3)^3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1 * G.2, G.4 * G.2 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.3 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.3 * G.1, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.1 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.2^-1 * G.3 * G.2 * G.1)^2, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2 * G.3 * G.1 * G.4, G.4^-3, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, (G.1 * G.4 * G.3 * G.4^-1)^2, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.4 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2^-1 * G.4^-1, G.3 * G.1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.2^-1 * G.4^-1 * G.1)^2, (G.4^-1 * G.2)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.1 * G.3 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.4 * G.3 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.2 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2^-1, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2 * G.4^-1, G.1 * G.2 * G.1 * G.3 * G.2 * G.1 * G.2^2 * G.1 * G.3 * G.1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.3 * G.1 * G.4 * G.3 * G.2 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.3)^4, G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2 * G.4 * G.2 * G.3 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.2, G.2 * G.4 * G.2 * G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1 * G.3 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4 * G.2 * G.4^-1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.3)^4, (G.4^-1 * G.2^-1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.3^2, G.4^-1 * G.2^-1, G.2^-3, G.2^-1 * G.1 * G.2 * G.3, (G.3 * G.1)^3, (G.1 * G.2^-1 * G.3)^10 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.4^-1)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, (G.3 * G.1)^3, G.1 * G.4 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2 * G.1 * G.4 * G.3 * G.4^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1, G.4^-1 * G.1 * G.4^-1 * G.2^-1 * G.3 * G.1 * G.2^2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, (G.2^-1 * G.1)^4, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1, (G.3 * G.1)^3, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.3 * G.2 * G.1 * G.3 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^2 * G.1 * G.2 * G.4 * G.2 * G.1 * G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.3, G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.1, G.4 * G.2^-1 * G.4^-1 * G.2^-1 * G.3 * G.4^-1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] [ G.1^2, G.2^-3, G.4^-1 * G.1 * G.2^-1 * G.1, (G.4^-1 * G.2^-1)^3, G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1, G.3 * G.1^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.3 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is reflexible [2] and there is a non-orientable quotient [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2^-1, (G.3 * G.1)^5 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2 * G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 * G.2 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.3 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, (G.2^-1 * G.1)^4, G.3 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.1, G.4 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.1 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.2^-1, G.3 * G.2 * G.1 * G.2^-1 * G.4 * G.2, G.3 * G.1 * G.4 * G.2^-1 * G.3 * G.1 * G.3 * G.2^-1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.4 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.1 * G.3 * G.1)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.1 * G.2 * G.4^-1 * G.2 * G.4^-1 * G.2 * G.4^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.3 * G.2, G.4 * G.2^-1 * G.1 * G.2 * G.4^-1 * G.1, G.1 * G.4 * G.2 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.2^-1 * G.1 * G.3 * G.1 * G.4 * G.2 * G.1 * G.3 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.1 * G.3 * G.2^-1 * G.3)^2, G.4 * G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.1 * G.2^-1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, (G.2^-1 * G.3)^4, G.4^-1 * G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 * G.2 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.1 * G.3)^2, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.2^-1 * G.4 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^2 * G.4 * G.2^-1 * G.4 * G.2^-1 * G.4 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^-3, (G.4^-1 * G.2^-1)^3, G.3 * G.1 * G.3 * G.2^-1 * G.4 * G.1 * G.4 * G.2^-1 * G.4 * G.2^2 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 * G.3 * G.1 ] Genus 101 action of group of order 600 via quadrangle group [ 2, 3, 2, 3 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^-3, (G.4^-1 * G.2^-1)^3, G.4^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.4 * G.3, G.4^-1 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.3, G.1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3, G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2^-1 * G.3 * G.4^-1, G.2^-1 * G.3 * G.1 * G.4^-1 * G.2 * G.3 * G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.3 * G.2 * G.3 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, (G.1 * G.3 * G.2^-1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1,2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2 * G.1 * G.2^-1 * G.1 * G.2 * G.1 * G.3 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, (G.2^-1 * G.3 * G.1 * G.3 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.4^-1 * G.2^-1 * G.4, G.4^4, G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3 * G.2 * G.3 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, (G.2^-1 * G.1 * G.3 * G.1)^2, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.4^-1 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2^-1 * G.1 * G.4, G.2^-1 * G.1 * G.3 * G.4 * G.2^-1 * G.1 * G.2 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4^-1 * G.1)^2, (G.2^-1 * G.4 * G.3)^2, G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.4 * G.2^-1 * G.4^-1, G.2 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, (G.4, G.2^-1, G.4) ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [2] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.3 * G.1 * G.2^-1 * G.1 * G.3, G.2 * G.4^-1 * G.2^-1 * G.4^-1 * G.2 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, G.2^-1 * G.4 * G.3 * G.2 * G.3 * G.4^-1, G.2^-1 * G.3 * G.2 * G.4^-1 * G.2 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2^-1 * G.3 * G.2 * G.4 * G.2 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, (G.2^-1 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, (G.2^-1 * G.1)^2, G.3 * G.1 * G.2 * G.4^-1, G.4^4, (G.2^-1 * G.3)^4, G.2^-1 * G.4 * G.2^-1 * G.3 * G.2 * G.4^-1 * G.1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, (G.2 * G.1 * G.2^-1 * G.1)^2, G.1 * G.3 * G.2 * G.1 * G.2^-1 * G.4^-1 * G.1 * G.2^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.2^-1 * G.3 * G.2 * G.3, G.4^4, (G.2 * G.1 * G.2^-1 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1, G.4 * G.3 * G.2 * G.1 * G.2^-1 * G.3 * G.4^-1 * G.1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, G.2 * G.4^-1 * G.2 * G.1 * G.2^-1 * G.4 * G.3 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.1 * G.4 * G.3)^2, G.1 * G.2 * G.1 * G.2^-1 * G.4 * G.2^-1 * G.4^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2^-1 * G.4^-1 * G.1)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, (G.2^-1 * G.1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, (G.2^-1 * G.1)^4, (G.2^-1 * G.4 * G.2^-1 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, (G.2^-1 * G.1)^4, (G.2^-1 * G.4^-1)^4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] and there is a non-orientable quotient [1] [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, (G.2^-1 * G.3)^2, G.4^4, G.2^-1 * G.4^-1 * G.1 * G.2 * G.1 * G.4, (G.2^-1 * G.1 * G.2^-1 * G.1 * G.2^-1 * G.1 * G.2 * G.1)^2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, G.2^-1 * G.4^-2 * G.2^-1 * G.4^2, G.4^-1 * G.1 * G.3 * G.1 * G.2^-1 * G.3 * G.1 * G.3 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1, G.3 * G.2 * G.3 * G.1 * G.2^-1 * G.3 * G.2^-1 * G.4 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, G.2 * G.4 * G.3 * G.2^-1 * G.3 * G.2 * G.4^-1, G.4^-2 * G.2^-1 * G.1 * G.2^-1 * G.4 * G.3 * G.2 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is chiral [ G.1^2, G.3^2, G.2^-3, G.4 * G.1 * G.2 * G.3, G.4^4, (G.2 * G.4 * G.3)^2, (G.1 * G.4 * G.3)^2, G.4^-1 * G.2 * G.4^-1 * G.2^-1 * G.4^2 * G.2^-1 ] Genus 101 action of group of order 480 via quadrangle group [ 2, 3, 2, 4 ] Action is reflexible [1] [ G.1^2, G.3^2, G.2^-3, G.2^-1 * G.1 * G.2 * G.1, G.3 * G.1 * G.2^-1 * G.4^-1, G.4^4, (G.2 * G.3 * G.2^-1 * G.3)^2 ] Largest orientation-preserving group for genus 101 has order 2400 ... group action with signature (0: +; [3,3,4]; {-}) Largest group with or without reflections for genus 101 has order 4800 ... group action with signature (0; +; [3]; {(4)}) Largest group with reflections for genus 101 has order 4800 ... group action with signature (0; +; [3]; {(4)}) Largest chiral group for genus 101 has order 2400 ... group action with signature (0: +; [3,3,4]; {-}) Largest non-orientable group for non-orientable genus 102 has order 1200 ... group action with signature (0; +; [-]; {(2,2,2,3)}) Check total 2555 : 1904 chiral, 651 reflexible, with 179 non-orientable quotient actions